{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m    Status\u001b[22m\u001b[39m `/mnt/E4E0A9C0E0A998F6/github/ReinforcementLearningAnIntroduction.jl/notebooks/Project.toml`\n",
      " \u001b[90m [31c24e10]\u001b[39m\u001b[37m Distributions v0.22.4\u001b[39m\n",
      " \u001b[90m [91a5bcdd]\u001b[39m\u001b[37m Plots v0.29.1\u001b[39m\n",
      " \u001b[90m [02c1da58]\u001b[39m\u001b[37m ReinforcementLearningAnIntroduction v0.2.0 [`..`]\u001b[39m\n",
      " \u001b[90m [2913bbd2]\u001b[39m\u001b[37m StatsBase v0.32.1\u001b[39m\n",
      " \u001b[90m [f3b207a7]\u001b[39m\u001b[37m StatsPlots v0.12.0\u001b[39m\n",
      " \u001b[90m [2f01184e]\u001b[39m\u001b[37m SparseArrays \u001b[39m\n"
     ]
    }
   ],
   "source": [
    "]st"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling Plots [91a5bcdd-55d7-5caf-9e0b-520d859cae80]\n",
      "└ @ Base loading.jl:1273\n",
      "┌ Info: Precompiling StatsPlots [f3b207a7-027a-5e70-b257-86293d7955fd]\n",
      "└ @ Base loading.jl:1273\n",
      "WARNING: could not import Tables.select into StatsPlots\n"
     ]
    }
   ],
   "source": [
    "using StatsBase\n",
    "using ReinforcementLearningAnIntroduction\n",
    "using Plots, StatsPlots\n",
    "\n",
    "default(size=(800, 600))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiArmBanditsEnv([2.207226272254229, 0.1638650732416387, 0.879220051837527, -1.4913967098375687, 0.16458264730620673, -0.28033457712591653, -1.3155153947166967, 0.7912351230950092, 0.6679596300401259, -1.0495775431687635], 0.0, 1, false, 0.0, false, DiscreteSpace{UnitRange{Int64}}(1:1), DiscreteSpace{UnitRange{Int64}}(1:10))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env = MultiArmBanditsEnv()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the possible rewards for each action first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "violin([randn(100) .+ x for x in env.truevalues], leg=false)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we define a customized hook first to collect the info that our action is the best one or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "struct CollectBestActions <: AbstractHook\n",
    "    isbest::Vector{Bool}\n",
    "    CollectBestActions() = new(Vector{Bool}())\n",
    "end\n",
    "\n",
    "(h::CollectBestActions)(::PostActStage, agent, env, obs) = push!(h.isbest, env.isbest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we create a testbed to explore the impact of different ϵ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bandit_testbed (generic function with 1 method)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function bandit_testbed(;explorer=EpsilonGreedyExplorer(0.1), truereward=0.0, init=0., opt=InvDecay(1.0))\n",
    "    env = MultiArmBanditsEnv(truereward=truereward)\n",
    "    agent = Agent(\n",
    "        policy=QBasedPolicy(\n",
    "            TDLearner(\n",
    "                approximator = TabularApproximator(\n",
    "                    n_state=length(get_observation_space(env)),\n",
    "                    n_action=length(get_action_space(env)),\n",
    "                    init=init\n",
    "                ),\n",
    "                optimizer = opt\n",
    "            ),\n",
    "            explorer\n",
    "        ),\n",
    "        trajectory=EpisodicCompactSARTSATrajectory()\n",
    "    )\n",
    "    best_action_stats, reward_stats = CollectBestActions(), RewardsPerEpisode()\n",
    "    run(agent, env, StopAfterStep(1000),ComposedHook(best_action_stats, reward_stats))\n",
    "    collect(Iterators.flatten(reward_stats.rewards)),best_action_stats.isbest\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:00\u001b[39m\n"
     ]
    },
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       "  1009.13,142.515 1011.95,149.819 1014.78,143.341 1017.6,167.209 1020.43,141.203 1023.25,171.463 1026.08,154.729 1028.9,167.02 1031.72,189.39 1034.55,162.114 \n",
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       "  1178.59,179.988 1181.42,180.269 1184.24,170.87 1187.07,171.823 1189.89,150.871 1192.72,131.578 1195.54,158.682 1198.36,147.478 1201.19,163.419 1204.01,144.665 \n",
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       "  1235.08,142.954 1237.91,166.827 1240.73,171.429 1243.55,172.357 1246.38,131.489 1249.2,154.546 1252.03,149.816 1254.85,141.619 1257.68,144.607 1260.5,152.241 \n",
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       "  1291.57,152.509 1294.39,158.309 1297.22,153.126 1300.04,156.283 1302.87,166.827 1305.69,148.032 1308.51,158.457 1311.34,149.741 1314.16,141.796 1316.99,129.311 \n",
       "  1319.81,133.549 1322.64,131.866 1325.46,134.781 1328.29,136.651 1331.11,154.059 1333.93,130.384 1336.76,189.766 1339.58,132.292 1342.41,174.356 1345.23,126.779 \n",
       "  1348.06,158.135 1350.88,163.132 1353.71,119.457 1356.53,159.524 1359.35,136.223 1362.18,174.226 1365,141.323 1367.83,127.399 1370.65,146 1373.48,160.422 \n",
       "  1376.3,159.487 1379.12,126.249 1381.95,137.631 1384.77,128.998 1387.6,151.386 1390.42,138.126 1393.25,160.925 1396.07,186.843 1398.9,124.002 1401.72,121.601 \n",
       "  1404.54,139.699 1407.37,127.566 1410.19,157.674 1413.02,127.182 1415.84,135.698 1418.67,138.406 1421.49,149.249 1424.31,138.988 1427.14,159.832 1429.96,170.068 \n",
       "  1432.79,149.981 1435.61,153.721 1438.44,100.723 1441.26,140.81 1444.09,141.217 1446.91,158.336 1449.73,141.219 1452.56,128.147 1455.38,177.373 1458.21,147.319 \n",
       "  1461.03,144.178 1463.86,129.307 1466.68,128.338 1469.51,152.556 1472.33,147.921 1475.15,160.984 1477.98,134.76 1480.8,167.221 1483.63,126.495 1486.45,130.195 \n",
       "  1489.28,154.206 1492.1,130.097 1494.92,124.445 1497.75,159.215 1500.57,136.858 1503.4,140.854 1506.22,115.298 1509.05,163.159 1511.87,160.111 1514.7,121.518 \n",
       "  1517.52,151.438 1520.34,159.7 1523.17,148.408 1525.99,146.605 1528.82,143.829 1531.64,143.671 1534.47,139.904 1537.29,106.393 1540.11,153.618 1542.94,125.663 \n",
       "  1545.76,153.493 1548.59,137.297 1551.41,110.774 1554.24,124.307 1557.06,149.778 1559.89,105.633 1562.71,154.08 1565.53,110.257 1568.36,129.504 1571.18,150.221 \n",
       "  1574.01,152.864 1576.83,122.616 1579.66,113.983 1582.48,137.62 1585.31,126.332 1588.13,150.651 1590.95,163.3 1593.78,115.318 1596.6,167.89 1599.43,135.912 \n",
       "  1602.25,86.4846 1605.08,148.723 1607.9,114.495 1610.72,98.5832 1613.55,171.906 1616.37,117.847 1619.2,123.171 1622.02,135.33 1624.85,164.779 1627.67,142.42 \n",
       "  1630.5,123.357 1633.32,147.101 1636.14,150.486 1638.97,153.059 1641.79,142.361 1644.62,150.39 1647.44,126.284 1650.27,116.761 1653.09,116.984 1655.91,172.195 \n",
       "  1658.74,120.375 1661.56,107.599 1664.39,109.326 1667.21,136.142 1670.04,121.111 1672.86,163.755 1675.69,141.26 1678.51,136.894 1681.33,148.45 1684.16,116.958 \n",
       "  1686.98,128.61 1689.81,152.601 1692.63,180.05 1695.46,141.949 1698.28,155.982 1701.1,123.524 1703.93,131.975 1706.75,137.744 1709.58,134.924 1712.4,131.026 \n",
       "  1715.23,107.551 1718.05,110.203 1720.88,147.218 1723.7,127.98 1726.52,164.867 1729.35,125.687 1732.17,143.157 1735,165.006 1737.82,158.047 1740.65,115.289 \n",
       "  1743.47,138.55 1746.3,143.721 1749.12,154.59 1751.94,142.446 1754.77,133.085 1757.59,129.072 1760.42,159.937 1763.24,110.602 1766.07,148.06 1768.89,108.122 \n",
       "  1771.71,160.56 1774.54,132.74 1777.36,110.351 1780.19,135.482 1783.01,135.035 1785.84,143.415 1788.66,138.893 1791.49,99.1632 1794.31,150.251 1797.13,111.017 \n",
       "  1799.96,146.225 1802.78,153.437 1805.61,147.51 1808.43,154.528 1811.26,156.579 1814.08,136.269 1816.9,131.293 1819.73,120.994 1822.55,119.781 1825.38,137.286 \n",
       "  1828.2,142.764 1831.03,144.024 1833.85,148.334 1836.68,126.886 1839.5,132.588 1842.32,118.222 1845.15,118.85 1847.97,118.648 1850.8,161.874 1853.62,118.484 \n",
       "  1856.45,145.674 1859.27,133.252 1862.1,154.124 1864.92,113.684 1867.74,151.144 1870.57,155.626 1873.39,145.079 1876.22,127.368 1879.04,154.286 1881.87,136.558 \n",
       "  1884.69,125.512 1887.51,161.157 1890.34,128.511 1893.16,138.677 1895.99,153.162 1898.81,148.78 1901.64,109.329 1904.46,130.606 1907.29,141.748 1910.11,140.947 \n",
       "  1912.93,131.908 1915.76,141.127 1918.58,125.854 1921.41,162.809 1924.23,123.515 1927.06,84.8235 1929.88,122.359 1932.7,123.788 1935.53,154.001 1938.35,94.9498 \n",
       "  1941.18,121.783 1944,105.563 1946.83,136.171 1949.65,145.193 1952.48,142.967 1955.3,138.255 1958.12,145.563 1960.95,157.441 1963.77,120.432 1966.6,139.329 \n",
       "  1969.42,139.151 1972.25,118.324 1975.07,162.93 1977.9,122.978 1980.72,124.71 1983.54,139.469 1986.37,111.352 1989.19,137.002 1992.02,116.886 1994.84,140.822 \n",
       "  1997.67,169.463 2000.49,140.127 2003.31,137.107 2006.14,122.214 2008.96,142.656 2011.79,113.778 2014.61,107.388 2017.44,97.8059 2020.26,123.622 2023.09,103.682 \n",
       "  2025.91,120.28 2028.73,162.142 2031.56,117.376 2034.38,124.696 2037.21,128.613 2040.03,122.647 2042.86,113.511 2045.68,135.126 2048.5,131.925 2051.33,152.265 \n",
       "  2054.15,143.323 2056.98,123.855 2059.8,145.336 2062.63,144.04 2065.45,111.893 2068.28,121.693 2071.1,112.998 2073.92,107.383 2076.75,139.989 2079.57,102.502 \n",
       "  2082.4,148.817 2085.22,111.722 2088.05,179.973 2090.87,127.44 2093.69,148.331 2096.52,148.342 2099.34,109.316 2102.17,130.264 2104.99,136.316 2107.82,147.638 \n",
       "  2110.64,99.4075 2113.47,106.227 2116.29,144.627 2119.11,117.8 2121.94,141.446 2124.76,135.576 2127.59,133.461 2130.41,118.702 2133.24,146.948 2136.06,136.486 \n",
       "  2138.89,142.322 2141.71,118.77 2144.53,131.744 2147.36,118.288 2150.18,127.006 2153.01,134.307 2155.83,150.529 2158.66,136.628 2161.48,114.159 2164.3,135.329 \n",
       "  2167.13,132.718 2169.95,138.229 2172.78,141.875 2175.6,119.366 2178.43,139.957 2181.25,116.634 2184.08,138.023 2186.9,112.164 2189.72,113.694 2192.55,103.417 \n",
       "  2195.37,130.084 2198.2,157.52 2201.02,156.371 2203.85,154.428 2206.67,114.704 2209.49,150.856 2212.32,148.604 2215.14,109.779 2217.97,132.169 2220.79,119.983 \n",
       "  2223.62,140.707 2226.44,106.615 2229.27,133.563 2232.09,146.591 2234.91,126.674 2237.74,125.839 2240.56,108.633 2243.39,136.757 2246.21,155.679 2249.04,107.653 \n",
       "  2251.86,127.489 2254.69,129.751 2257.51,131.431 2260.33,109.917 2263.16,144.349 2265.98,114.258 2268.81,123.351 2271.63,154.059 2274.46,117.407 2277.28,127.619 \n",
       "  2280.1,165.206 2282.93,125.537 2285.75,126.173 2288.58,144.749 2291.4,148.517 2294.23,146.804 2297.05,154.078 2299.88,134.231 2302.7,143.306 2305.52,137.57 \n",
       "  2308.35,142.782 2311.17,151.38 2314,135.42 2316.82,117.603 2319.65,115.309 2322.47,105.851 2325.29,129.84 2328.12,132.247 2330.94,102.115 2333.77,128.707 \n",
       "  2336.59,120.986 2339.42,138.019 2342.24,136.543 2345.07,105.296 2347.89,121.57 2350.71,117.71 2353.54,160.064 2356.36,100.484 2359.19,138.61 2362.01,137.227 \n",
       "  2364.84,137.162 2367.66,118.335 2370.49,121.267 2373.31,104.754 2376.13,134.718 2378.96,145.787 2381.78,138.05 2384.61,122.641 2387.43,105.561 2390.26,149.238 \n",
       "  2393.08,130.107 2395.9,113.914 2398.73,139.689 2401.55,131.184 2404.38,142.454 2407.2,130.078 2410.03,123.341 2412.85,160.159 2415.68,175.301 2418.5,120.12 \n",
       "  2421.32,160.334 2424.15,100.314 2426.97,93.5265 2429.8,169.188 2432.62,128.715 2435.45,120.999 2438.27,136.311 2441.09,97.75 2443.92,150.594 2446.74,137.008 \n",
       "  2449.57,140.774 2452.39,92.832 2455.22,136.251 2458.04,136.694 2460.87,122.363 2463.69,155.251 2466.51,130.314 2469.34,123.464 2472.16,139.015 2474.99,102.737 \n",
       "  2477.81,140.262 2480.64,124.564 2483.46,106.92 2486.28,150.718 2489.11,151.87 2491.93,110.071 2494.76,127.772 2497.58,137.607 2500.41,115.794 2503.23,140.836 \n",
       "  2506.06,120.475 2508.88,122.795 2511.7,130.815 2514.53,99.2253 2517.35,121.048 2520.18,147.574 2523,132.627 2525.83,137.836 2528.65,160.102 2531.48,126.719 \n",
       "  2534.3,127.537 2537.12,139.181 2539.95,138.124 2542.77,122.166 2545.6,99.2898 2548.42,136.345 2551.25,124.731 2554.07,164.297 2556.89,106.788 2559.72,133.44 \n",
       "  2562.54,161.203 2565.37,121.454 2568.19,137.914 2571.02,126.01 2573.84,123.698 2576.67,132.095 2579.49,130.48 2582.31,109.419 2585.14,126.217 2587.96,126.507 \n",
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       "  1743.47,210.429 1746.3,228.35 1749.12,235.671 1751.94,211.682 1754.77,191.456 1757.59,200.826 1760.42,207.682 1763.24,203.316 1766.07,227.538 1768.89,203.379 \n",
       "  1771.71,189.384 1774.54,195.443 1777.36,205.433 1780.19,206.347 1783.01,199.278 1785.84,221.255 1788.66,199.359 1791.49,195.385 1794.31,211.212 1797.13,222.164 \n",
       "  1799.96,221.294 1802.78,203.341 1805.61,209.451 1808.43,207.092 1811.26,180.797 1814.08,186.604 1816.9,194.155 1819.73,206.323 1822.55,200.219 1825.38,205.629 \n",
       "  1828.2,178.14 1831.03,230.014 1833.85,192.656 1836.68,206.98 1839.5,209.662 1842.32,224.383 1845.15,218.77 1847.97,210.19 1850.8,217.371 1853.62,216.451 \n",
       "  1856.45,184.851 1859.27,192.823 1862.1,207.379 1864.92,215.821 1867.74,213.708 1870.57,188.031 1873.39,212.031 1876.22,181.924 1879.04,207.899 1881.87,216.767 \n",
       "  1884.69,195.341 1887.51,220.515 1890.34,195.557 1893.16,187.361 1895.99,214.622 1898.81,212.665 1901.64,203.683 1904.46,203.335 1907.29,188.231 1910.11,219.396 \n",
       "  1912.93,233.095 1915.76,195.014 1918.58,227.72 1921.41,197.382 1924.23,180.857 1927.06,198.364 1929.88,192.952 1932.7,175.591 1935.53,214.715 1938.35,194.381 \n",
       "  1941.18,202.574 1944,201.345 1946.83,182.955 1949.65,153.038 1952.48,186.914 1955.3,175.393 1958.12,215.116 1960.95,201.532 1963.77,207.704 1966.6,185.498 \n",
       "  1969.42,202.639 1972.25,195.653 1975.07,200.902 1977.9,191.896 1980.72,202.735 1983.54,202.213 1986.37,194.069 1989.19,208.678 1992.02,185.149 1994.84,176.05 \n",
       "  1997.67,194.537 2000.49,192.724 2003.31,200.005 2006.14,204.914 2008.96,190.517 2011.79,192.259 2014.61,198.5 2017.44,204.832 2020.26,206.288 2023.09,205.52 \n",
       "  2025.91,201.157 2028.73,203.237 2031.56,212.153 2034.38,194.095 2037.21,188.256 2040.03,216.944 2042.86,212.892 2045.68,190.899 2048.5,192.961 2051.33,220.674 \n",
       "  2054.15,175.127 2056.98,197.739 2059.8,226.483 2062.63,194.389 2065.45,188.819 2068.28,188.73 2071.1,219.02 2073.92,205.752 2076.75,192.965 2079.57,205.227 \n",
       "  2082.4,192.395 2085.22,188.343 2088.05,195.755 2090.87,199.319 2093.69,194.336 2096.52,213.512 2099.34,189.375 2102.17,156.918 2104.99,206.046 2107.82,178.822 \n",
       "  2110.64,214.598 2113.47,190.833 2116.29,179.295 2119.11,190.192 2121.94,172.763 2124.76,182.25 2127.59,203.792 2130.41,165.236 2133.24,186.897 2136.06,174.347 \n",
       "  2138.89,165.083 2141.71,159.633 2144.53,171.747 2147.36,171.749 2150.18,189.019 2153.01,172.287 2155.83,198.201 2158.66,185.88 2161.48,181.525 2164.3,172.669 \n",
       "  2167.13,181.163 2169.95,185.533 2172.78,178.922 2175.6,147.215 2178.43,199.914 2181.25,166.832 2184.08,199.328 2186.9,171.502 2189.72,188.001 2192.55,170.321 \n",
       "  2195.37,167.999 2198.2,170.163 2201.02,176.423 2203.85,157.523 2206.67,178.869 2209.49,181.922 2212.32,172.638 2215.14,153.543 2217.97,197.346 2220.79,197.251 \n",
       "  2223.62,177.781 2226.44,184.46 2229.27,172.415 2232.09,189.957 2234.91,163.811 2237.74,159.946 2240.56,183.66 2243.39,199.653 2246.21,215.161 2249.04,148.85 \n",
       "  2251.86,190.471 2254.69,162.424 2257.51,170.805 2260.33,169.547 2263.16,180.961 2265.98,171.407 2268.81,183.558 2271.63,180.421 2274.46,177.842 2277.28,182.658 \n",
       "  2280.1,177.052 2282.93,161.925 2285.75,186.107 2288.58,185.216 2291.4,162.375 2294.23,185.982 2297.05,190.724 2299.88,178.492 2302.7,172.975 2305.52,177.207 \n",
       "  2308.35,164.4 2311.17,179.022 2314,166.687 2316.82,184.72 2319.65,193.161 2322.47,190.708 2325.29,162.916 2328.12,171.317 2330.94,177.371 2333.77,165.005 \n",
       "  2336.59,163.606 2339.42,180.186 2342.24,175.104 2345.07,198.575 2347.89,176.802 2350.71,165.155 2353.54,164.704 2356.36,185.656 2359.19,168.984 2362.01,166.684 \n",
       "  2364.84,196.541 2367.66,188.21 2370.49,177.117 2373.31,170.621 2376.13,198.257 2378.96,178.593 2381.78,155.605 2384.61,176.008 2387.43,180.755 2390.26,160.437 \n",
       "  2393.08,172.488 2395.9,182.876 2398.73,176.972 2401.55,185.533 2404.38,207.132 2407.2,145.225 2410.03,167.102 2412.85,171.934 2415.68,158.381 2418.5,174.378 \n",
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       "  2477.81,181.376 2480.64,177.46 2483.46,174.837 2486.28,199.68 2489.11,163.604 2491.93,203.908 2494.76,195.221 2497.58,157.371 2500.41,174.18 2503.23,170.609 \n",
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       "  1574.01,317.19 1576.83,301.653 1579.66,357.918 1582.48,321.226 1585.31,323.259 1588.13,330.111 1590.95,323.729 1593.78,321.279 1596.6,339.78 1599.43,330.615 \n",
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       "  1715.23,348.394 1718.05,295.551 1720.88,314.55 1723.7,328.939 1726.52,338.945 1729.35,329.548 1732.17,313.991 1735,322.218 1737.82,315.725 1740.65,333.657 \n",
       "  1743.47,321.412 1746.3,306.97 1749.12,318.117 1751.94,332.233 1754.77,327.181 1757.59,326.72 1760.42,338.752 1763.24,334.162 1766.07,327.807 1768.89,350.311 \n",
       "  1771.71,289.688 1774.54,330.096 1777.36,312.325 1780.19,333.408 1783.01,373.112 1785.84,312.641 1788.66,337.493 1791.49,327.181 1794.31,342.365 1797.13,336.38 \n",
       "  1799.96,340.794 1802.78,338.363 1805.61,324.8 1808.43,312.028 1811.26,340.297 1814.08,327.576 1816.9,329.223 1819.73,326.24 1822.55,338.215 1825.38,335.935 \n",
       "  1828.2,344.658 1831.03,337.187 1833.85,314.395 1836.68,311.797 1839.5,337.231 1842.32,319.525 1845.15,324.539 1847.97,327.269 1850.8,320.997 1853.62,313.004 \n",
       "  1856.45,355.8 1859.27,309.199 1862.1,319.441 1864.92,346.61 1867.74,316.152 1870.57,337.988 1873.39,338.917 1876.22,319.483 1879.04,322.241 1881.87,337.623 \n",
       "  1884.69,315.996 1887.51,319.746 1890.34,318.68 1893.16,343.837 1895.99,310.066 1898.81,334.301 1901.64,342.139 1904.46,320.854 1907.29,326.373 1910.11,329.747 \n",
       "  1912.93,308.698 1915.76,332.351 1918.58,337.367 1921.41,333.322 1924.23,324.582 1927.06,316.256 1929.88,306.42 1932.7,330.119 1935.53,349.309 1938.35,334.93 \n",
       "  1941.18,337.261 1944,329.184 1946.83,312.916 1949.65,332.377 1952.48,343.443 1955.3,302.22 1958.12,326.167 1960.95,315.346 1963.77,349.281 1966.6,328.606 \n",
       "  1969.42,317.252 1972.25,320.909 1975.07,316.227 1977.9,307.66 1980.72,316.216 1983.54,322.562 1986.37,327.276 1989.19,333.592 1992.02,331.07 1994.84,325.974 \n",
       "  1997.67,324.101 2000.49,344.507 2003.31,329.576 2006.14,337.049 2008.96,329.816 2011.79,336.231 2014.61,343.955 2017.44,317.83 2020.26,328.905 2023.09,309.365 \n",
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       "  1489.28,1374.55 1492.1,1367.05 1494.92,1360.91 1497.75,1367.73 1500.57,1370.46 1503.4,1360.23 1506.22,1363.64 1509.05,1383.42 1511.87,1360.91 1514.7,1362.28 \n",
       "  1517.52,1361.59 1520.34,1360.91 1523.17,1379.33 1525.99,1373.87 1528.82,1369.78 1531.64,1376.6 1534.47,1361.59 1537.29,1360.91 1540.11,1367.73 1542.94,1358.87 \n",
       "  1545.76,1361.59 1548.59,1365 1551.41,1364.32 1554.24,1353.41 1557.06,1368.41 1559.89,1344.54 1562.71,1358.18 1565.53,1358.87 1568.36,1355.46 1571.18,1352.04 \n",
       "  1574.01,1366.37 1576.83,1346.59 1579.66,1362.28 1582.48,1363.64 1585.31,1354.09 1588.13,1365.69 1590.95,1367.05 1593.78,1348.63 1596.6,1371.82 1599.43,1362.96 \n",
       "  1602.25,1345.22 1605.08,1362.96 1607.9,1354.77 1610.72,1351.36 1613.55,1371.82 1616.37,1356.14 1619.2,1352.73 1622.02,1348.63 1624.85,1355.46 1627.67,1353.41 \n",
       "  1630.5,1351.36 1633.32,1360.91 1636.14,1355.46 1638.97,1361.59 1641.79,1343.18 1644.62,1347.95 1647.44,1356.82 1650.27,1354.77 1653.09,1347.27 1655.91,1356.14 \n",
       "  1658.74,1349.32 1661.56,1332.27 1664.39,1356.14 1667.21,1354.77 1670.04,1348.63 1672.86,1341.81 1675.69,1356.82 1678.51,1362.96 1681.33,1354.77 1684.16,1356.82 \n",
       "  1686.98,1354.77 1689.81,1356.82 1692.63,1358.87 1695.46,1348.63 1698.28,1345.91 1701.1,1333.63 1703.93,1338.4 1706.75,1350.68 1709.58,1337.04 1712.4,1347.95 \n",
       "  1715.23,1354.77 1718.05,1340.45 1720.88,1344.54 1723.7,1357.5 1726.52,1353.41 1729.35,1339.09 1732.17,1344.54 1735,1334.31 1737.82,1352.73 1740.65,1329.54 \n",
       "  1743.47,1341.13 1746.3,1356.82 1749.12,1352.73 1751.94,1339.77 1754.77,1345.91 1757.59,1334.99 1760.42,1357.5 1763.24,1334.99 1766.07,1340.45 1768.89,1327.49 \n",
       "  1771.71,1339.77 1774.54,1343.86 1777.36,1324.76 1780.19,1347.95 1783.01,1332.27 1785.84,1341.13 1788.66,1334.31 1791.49,1338.4 1794.31,1332.95 1797.13,1339.77 \n",
       "  1799.96,1333.63 1802.78,1355.46 1805.61,1341.13 1808.43,1328.86 1811.26,1333.63 1814.08,1341.81 1816.9,1321.35 1819.73,1333.63 1822.55,1329.54 1825.38,1324.08 \n",
       "  1828.2,1349.32 1831.03,1342.5 1833.85,1322.04 1836.68,1331.58 1839.5,1336.36 1842.32,1337.04 1845.15,1337.04 1847.97,1336.36 1850.8,1331.58 1853.62,1328.17 \n",
       "  1856.45,1340.45 1859.27,1339.09 1862.1,1333.63 1864.92,1319.99 1867.74,1332.27 1870.57,1335.68 1873.39,1330.9 1876.22,1346.59 1879.04,1343.18 1881.87,1324.08 \n",
       "  1884.69,1336.36 1887.51,1340.45 1890.34,1339.77 1893.16,1341.13 1895.99,1350 1898.81,1341.13 1901.64,1331.58 1904.46,1334.31 1907.29,1351.36 1910.11,1339.09 \n",
       "  1912.93,1346.59 1915.76,1332.95 1918.58,1348.63 1921.41,1339.77 1924.23,1337.04 1927.06,1330.9 1929.88,1328.86 1932.7,1341.13 1935.53,1332.27 1938.35,1326.13 \n",
       "  1941.18,1315.9 1944,1322.72 1946.83,1331.58 1949.65,1346.59 1952.48,1343.18 1955.3,1341.13 1958.12,1341.13 1960.95,1336.36 1963.77,1337.72 1966.6,1333.63 \n",
       "  1969.42,1326.81 1972.25,1317.94 1975.07,1334.99 1977.9,1331.58 1980.72,1331.58 1983.54,1337.04 1986.37,1317.94 1989.19,1325.45 1992.02,1328.17 1994.84,1339.09 \n",
       "  1997.67,1346.59 2000.49,1334.31 2003.31,1334.31 2006.14,1332.27 2008.96,1325.45 2011.79,1333.63 2014.61,1318.63 2017.44,1331.58 2020.26,1334.99 2023.09,1315.9 \n",
       "  2025.91,1334.31 2028.73,1336.36 2031.56,1330.9 2034.38,1322.04 2037.21,1319.99 2040.03,1323.4 2042.86,1324.08 2045.68,1317.94 2048.5,1334.31 2051.33,1332.95 \n",
       "  2054.15,1319.99 2056.98,1331.58 2059.8,1334.31 2062.63,1334.99 2065.45,1324.08 2068.28,1331.58 2071.1,1337.04 2073.92,1303.62 2076.75,1337.72 2079.57,1324.76 \n",
       "  2082.4,1339.09 2085.22,1334.31 2088.05,1337.72 2090.87,1321.35 2093.69,1333.63 2096.52,1339.09 2099.34,1316.58 2102.17,1311.12 2104.99,1334.31 2107.82,1329.54 \n",
       "  2110.64,1317.26 2113.47,1315.22 2116.29,1340.45 2119.11,1321.35 2121.94,1332.27 2124.76,1315.22 2127.59,1324.76 2130.41,1326.13 2133.24,1328.86 2136.06,1326.81 \n",
       "  2138.89,1319.99 2141.71,1319.31 2144.53,1324.76 2147.36,1328.86 2150.18,1326.81 2153.01,1319.31 2155.83,1318.63 2158.66,1337.72 2161.48,1314.53 2164.3,1323.4 \n",
       "  2167.13,1323.4 2169.95,1321.35 2172.78,1331.58 2175.6,1328.86 2178.43,1322.04 2181.25,1322.72 2184.08,1329.54 2186.9,1317.26 2189.72,1313.85 2192.55,1317.26 \n",
       "  2195.37,1317.26 2198.2,1334.31 2201.02,1332.27 2203.85,1330.22 2206.67,1318.63 2209.49,1331.58 2212.32,1339.77 2215.14,1317.26 2217.97,1332.27 2220.79,1343.86 \n",
       "  2223.62,1330.22 2226.44,1317.94 2229.27,1344.54 2232.09,1326.13 2234.91,1324.08 2237.74,1321.35 2240.56,1316.58 2243.39,1331.58 2246.21,1330.22 2249.04,1324.76 \n",
       "  2251.86,1319.31 2254.69,1324.08 2257.51,1319.31 2260.33,1324.76 2263.16,1324.76 2265.98,1330.22 2268.81,1308.39 2271.63,1319.99 2274.46,1313.85 2277.28,1323.4 \n",
       "  2280.1,1321.35 2282.93,1311.12 2285.75,1313.17 2288.58,1318.63 2291.4,1323.4 2294.23,1329.54 2297.05,1322.72 2299.88,1317.94 2302.7,1320.67 2305.52,1334.31 \n",
       "  2308.35,1324.08 2311.17,1314.53 2314,1326.81 2316.82,1322.04 2319.65,1319.99 2322.47,1318.63 2325.29,1310.44 2328.12,1312.49 2330.94,1308.39 2333.77,1302.26 \n",
       "  2336.59,1310.44 2339.42,1321.35 2342.24,1327.49 2345.07,1303.62 2347.89,1302.26 2350.71,1318.63 2353.54,1325.45 2356.36,1310.44 2359.19,1319.99 2362.01,1325.45 \n",
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       "  2082.4,1639.86 2085.22,1639.18 2088.05,1635.09 2090.87,1640.54 2093.69,1635.77 2096.52,1640.54 2099.34,1636.45 2102.17,1633.72 2104.99,1635.77 2107.82,1636.45 \n",
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       "  2364.84,1603.03 2367.66,1600.99 2370.49,1603.03 2373.31,1601.67 2376.13,1604.4 2378.96,1605.76 2381.78,1601.67 2384.61,1603.71 2387.43,1598.26 2390.26,1595.53 \n",
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       "  2421.32,1595.53 2424.15,1598.26 2426.97,1601.67 2429.8,1596.21 2432.62,1594.85 2435.45,1597.58 2438.27,1597.58 2441.09,1596.21 2443.92,1593.48 2446.74,1593.48 \n",
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       "  2562.54,1585.98 2565.37,1585.3 2568.19,1584.62 2571.02,1581.21 2573.84,1584.62 2576.67,1588.03 2579.49,1585.98 2582.31,1581.21 2585.14,1585.98 2587.96,1584.62 \n",
       "  2590.79,1585.98 2593.61,1585.98 2596.44,1579.84 2599.26,1582.57 2602.08,1579.16 2604.91,1581.89 2607.73,1579.16 2610.56,1577.12 2613.38,1581.21 2616.21,1582.57 \n",
       "  2619.03,1579.84 2621.86,1579.16 2624.68,1578.48 2627.5,1579.84 2630.33,1579.16 2633.15,1581.89 2635.98,1577.8 2638.8,1580.53 2641.63,1574.39 2644.45,1577.12 \n",
       "  2647.28,1578.48 2650.1,1579.84 2652.92,1578.48 2655.75,1580.53 2658.57,1577.8 2661.4,1575.75 2664.22,1577.12 2667.05,1577.12 2669.87,1577.8 2672.69,1577.8 \n",
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       "  3042.69,1550.52 3045.51,1555.97 3048.34,1551.88 3051.16,1550.52 3053.99,1551.2 3056.81,1545.74 3059.64,1548.47 3062.46,1549.15 3065.28,1551.2 3068.11,1545.74 \n",
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     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(layout=(2, 1))\n",
    "for ϵ in [0.1, 0.01, 0.0]\n",
    "    stats = [bandit_testbed(;explorer=EpsilonGreedyExplorer(ϵ)) for _ in 1:2000]\n",
    "    plot!(p, mean(x[1] for x in stats), subplot=1, legend=:bottomright, label=\"epsilon=$ϵ\")\n",
    "    plot!(p, mean(x[2] for x in stats), subplot=2, legend=:bottomright, label=\"epsilon=$ϵ\")\n",
    "end\n",
    "\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:00\u001b[39m\n"
     ]
    },
    {
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       "  528.984,1609.75 531.808,1635.41 534.633,1620.55 537.457,1615.15 540.281,1634.06 543.106,1605.69 545.93,1588.13 548.754,1528.69 551.579,1563.82 554.403,1562.47 \n",
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       "  585.472,1407.12 588.296,1440.89 591.12,1434.14 593.945,1430.08 596.769,1438.19 599.593,1423.33 602.418,1407.12 605.242,1415.22 608.067,1400.36 610.891,1407.12 \n",
       "  613.715,1386.86 616.54,1373.35 619.364,1313.91 622.189,1323.37 625.013,1319.31 627.837,1354.44 630.662,1316.61 633.486,1338.23 636.311,1288.24 639.135,1286.89 \n",
       "  641.959,1265.28 644.784,1266.63 647.608,1235.56 650.432,1227.46 653.257,1204.49 656.081,1240.96 658.906,1219.35 661.73,1172.07 664.554,1195.03 667.379,1182.88 \n",
       "  670.203,1213.95 673.028,1174.77 675.852,1158.56 678.676,1141 681.501,1141 684.325,1127.49 687.149,1134.25 689.974,1116.69 692.798,1126.14 695.623,1128.84 \n",
       "  698.447,1127.49 701.271,1095.07 704.096,1081.56 706.92,1066.7 709.745,1078.86 712.569,1082.91 715.393,1086.97 718.218,1095.07 721.042,1059.95 723.867,1030.23 \n",
       "  726.691,1032.93 729.515,1030.23 732.34,999.162 735.164,978.899 737.988,970.794 740.813,968.092 743.637,950.531 746.462,937.022 749.286,938.373 752.11,932.97 \n",
       "  754.935,903.251 757.759,888.392 760.584,904.602 763.408,915.409 766.232,897.848 769.057,897.848 771.881,881.638 774.706,878.936 777.53,837.059 780.354,831.656 \n",
       "  783.179,833.007 786.003,814.095 788.827,795.183 791.652,812.744 794.476,795.183 797.301,801.937 800.125,791.131 802.949,783.025 805.774,765.464 808.598,777.622 \n",
       "  811.423,795.183 814.247,795.183 817.071,788.429 819.896,783.025 822.72,762.763 825.545,758.71 828.369,760.061 831.193,734.395 834.018,714.132 836.842,715.483 \n",
       "  839.666,681.712 842.491,701.974 845.315,693.869 848.14,683.062 850.964,668.203 853.788,683.062 856.613,662.8 859.437,658.747 862.262,651.993 865.086,653.344 \n",
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       "  896.154,658.747 898.979,664.151 901.803,634.432 904.627,622.274 907.452,650.642 910.276,650.642 913.101,656.045 915.925,635.783 918.749,620.923 921.574,637.134 \n",
       "  924.398,618.222 927.223,633.081 930.047,620.923 932.871,626.327 935.696,604.713 938.52,610.117 941.344,620.923 944.169,616.871 946.993,597.959 949.818,602.011 \n",
       "  952.642,589.854 955.466,569.591 958.291,549.328 961.115,569.591 963.94,573.644 966.764,579.047 969.588,564.188 972.413,564.188 975.237,558.784 978.062,557.433 \n",
       "  980.886,550.679 983.71,561.486 986.535,550.679 989.359,542.574 992.183,531.767 995.008,520.96 997.832,492.593 1000.66,499.347 1003.48,497.996 1006.31,496.645 \n",
       "  1009.13,514.206 1011.95,512.855 1014.78,514.206 1017.6,533.118 1020.43,531.767 1023.25,531.767 1026.08,533.118 1028.9,529.065 1031.72,527.715 1034.55,529.065 \n",
       "  1037.37,527.715 1040.2,506.101 1043.02,485.838 1045.85,484.487 1048.67,470.979 1051.5,457.47 1054.32,460.172 1057.14,450.716 1059.97,469.628 1062.79,466.926 \n",
       "  1065.62,481.786 1068.44,475.031 1071.27,481.786 1074.09,473.681 1076.92,454.769 1079.74,439.909 1082.56,458.821 1085.39,452.067 1088.21,453.418 1091.04,443.962 \n",
       "  1093.86,446.664 1096.69,445.313 1099.51,461.523 1102.33,431.804 1105.16,430.453 1107.98,412.892 1110.81,416.945 1113.63,430.453 1116.46,425.05 1119.28,435.857 \n",
       "  1122.11,433.155 1124.93,426.401 1127.75,426.401 1130.58,403.436 1133.4,406.138 1136.23,403.436 1139.05,402.086 1141.88,400.735 1144.7,402.086 1147.52,410.191 \n",
       "  1150.35,398.033 1153.17,415.594 1156,403.436 1158.82,399.384 1161.65,380.472 1164.47,371.016 1167.3,383.174 1170.12,402.086 1172.94,398.033 1175.77,399.384 \n",
       "  1178.59,393.98 1181.42,388.577 1184.24,383.174 1187.07,398.033 1189.89,389.928 1192.72,385.875 1195.54,375.069 1198.36,395.331 1201.19,399.384 1204.01,395.331 \n",
       "  1206.84,385.875 1209.66,385.875 1212.49,380.472 1215.31,389.928 1218.13,380.472 1220.96,372.367 1223.78,380.472 1226.61,380.472 1229.43,369.665 1232.26,366.963 \n",
       "  1235.08,360.209 1237.91,354.806 1240.73,346.701 1243.55,333.192 1246.38,325.087 1249.2,334.543 1252.03,329.14 1254.85,329.14 1257.68,319.684 1260.5,321.034 \n",
       "  1263.32,322.385 1266.15,316.982 1268.97,308.877 1271.8,323.736 1274.62,318.333 1277.45,325.087 1280.27,319.684 1283.1,302.123 1285.92,311.579 1288.74,319.684 \n",
       "  1291.57,321.034 1294.39,321.034 1297.22,335.894 1300.04,337.245 1302.87,331.841 1305.69,335.894 1308.51,333.192 1311.34,331.841 1314.16,345.35 1316.99,338.596 \n",
       "  1319.81,319.684 1322.64,323.736 1325.46,312.929 1328.29,299.421 1331.11,288.614 1333.93,296.719 1336.76,300.772 1339.58,308.877 1342.41,308.877 1345.23,304.824 \n",
       "  1348.06,306.175 1350.88,300.772 1353.71,292.667 1356.53,284.562 1359.35,283.211 1362.18,281.86 1365,276.456 1367.83,289.965 1370.65,285.912 1373.48,287.263 \n",
       "  1376.3,283.211 1379.12,269.702 1381.95,264.299 1384.77,262.948 1387.6,277.807 1390.42,283.211 1393.25,272.404 1396.07,273.755 1398.9,267 1401.72,269.702 \n",
       "  1404.54,267 1407.37,264.299 1410.19,262.948 1413.02,275.106 1415.84,273.755 1418.67,268.351 1421.49,271.053 1424.31,272.404 1427.14,271.053 1429.96,272.404 \n",
       "  1432.79,277.807 1435.61,264.299 1438.44,276.456 1441.26,269.702 1444.09,272.404 1446.91,291.316 1449.73,288.614 1452.56,296.719 1455.38,294.017 1458.21,295.368 \n",
       "  1461.03,287.263 1463.86,288.614 1466.68,295.368 1469.51,292.667 1472.33,280.509 1475.15,277.807 1477.98,280.509 1480.8,284.562 1483.63,280.509 1486.45,280.509 \n",
       "  1489.28,275.106 1492.1,271.053 1494.92,284.562 1497.75,276.456 1500.57,281.86 1503.4,285.912 1506.22,283.211 1509.05,275.106 1511.87,272.404 1514.7,283.211 \n",
       "  1517.52,285.912 1520.34,308.877 1523.17,298.07 1525.99,298.07 1528.82,291.316 1531.64,299.421 1534.47,296.719 1537.29,292.667 1540.11,295.368 1542.94,304.824 \n",
       "  1545.76,288.614 1548.59,296.719 1551.41,310.228 1554.24,310.228 1557.06,308.877 1559.89,295.368 1562.71,283.211 1565.53,280.509 1568.36,275.106 1571.18,277.807 \n",
       "  1574.01,276.456 1576.83,272.404 1579.66,291.316 1582.48,298.07 1585.31,289.965 1588.13,284.562 1590.95,276.456 1593.78,277.807 1596.6,277.807 1599.43,273.755 \n",
       "  1602.25,285.912 1605.08,276.456 1607.9,281.86 1610.72,284.562 1613.55,271.053 1616.37,276.456 1619.2,265.65 1622.02,267 1624.85,276.456 1627.67,271.053 \n",
       "  1630.5,268.351 1633.32,265.65 1636.14,261.597 1638.97,268.351 1641.79,269.702 1644.62,275.106 1647.44,264.299 1650.27,261.597 1653.09,258.895 1655.91,271.053 \n",
       "  1658.74,269.702 1661.56,271.053 1664.39,272.404 1667.21,276.456 1670.04,273.755 1672.86,285.912 1675.69,277.807 1678.51,279.158 1681.33,262.948 1684.16,257.545 \n",
       "  1686.98,260.246 1689.81,260.246 1692.63,264.299 1695.46,258.895 1698.28,257.545 1701.1,254.843 1703.93,254.843 1706.75,256.194 1709.58,248.089 1712.4,238.633 \n",
       "  1715.23,248.089 1718.05,246.738 1720.88,253.492 1723.7,242.685 1726.52,252.141 1729.35,252.141 1732.17,253.492 1735,252.141 1737.82,249.439 1740.65,239.983 \n",
       "  1743.47,241.334 1746.3,246.738 1749.12,246.738 1751.94,245.387 1754.77,245.387 1757.59,258.895 1760.42,257.545 1763.24,252.141 1766.07,250.79 1768.89,248.089 \n",
       "  1771.71,249.439 1774.54,245.387 1777.36,239.983 1780.19,241.334 1783.01,231.878 1785.84,229.177 1788.66,229.177 1791.49,231.878 1794.31,234.58 1797.13,227.826 \n",
       "  1799.96,222.422 1802.78,226.475 1805.61,210.265 1808.43,214.317 1811.26,215.668 1814.08,218.37 1816.9,221.072 1819.73,233.229 1822.55,219.721 1825.38,227.826 \n",
       "  1828.2,218.37 1831.03,221.072 1833.85,223.773 1836.68,231.878 1839.5,227.826 1842.32,227.826 1845.15,229.177 1847.97,229.177 1850.8,227.826 1853.62,233.229 \n",
       "  1856.45,223.773 1859.27,223.773 1862.1,222.422 1864.92,219.721 1867.74,211.616 1870.57,215.668 1873.39,212.966 1876.22,218.37 1879.04,221.072 1881.87,229.177 \n",
       "  1884.69,222.422 1887.51,222.422 1890.34,223.773 1893.16,231.878 1895.99,227.826 1898.81,229.177 1901.64,233.229 1904.46,227.826 1907.29,227.826 1910.11,234.58 \n",
       "  1912.93,229.177 1915.76,221.072 1918.58,218.37 1921.41,218.37 1924.23,210.265 1927.06,206.212 1929.88,200.809 1932.7,192.704 1935.53,196.756 1938.35,195.405 \n",
       "  1941.18,191.353 1944,191.353 1946.83,184.599 1949.65,192.704 1952.48,192.704 1955.3,192.704 1958.12,191.353 1960.95,191.353 1963.77,192.704 1966.6,195.405 \n",
       "  1969.42,200.809 1972.25,199.458 1975.07,198.107 1977.9,194.055 1980.72,190.002 1983.54,192.704 1986.37,194.055 1989.19,190.002 1992.02,191.353 1994.84,191.353 \n",
       "  1997.67,194.055 2000.49,194.055 2003.31,195.405 2006.14,191.353 2008.96,202.16 2011.79,198.107 2014.61,202.16 2017.44,203.51 2020.26,200.809 2023.09,200.809 \n",
       "  2025.91,194.055 2028.73,194.055 2031.56,191.353 2034.38,188.651 2037.21,184.599 2040.03,188.651 2042.86,195.405 2045.68,195.405 2048.5,192.704 2051.33,191.353 \n",
       "  2054.15,198.107 2056.98,202.16 2059.8,195.405 2062.63,185.949 2065.45,190.002 2068.28,187.3 2071.1,188.651 2073.92,183.248 2076.75,175.143 2079.57,183.248 \n",
       "  2082.4,191.353 2085.22,179.195 2088.05,187.3 2090.87,183.248 2093.69,180.546 2096.52,172.441 2099.34,175.143 2102.17,177.844 2104.99,183.248 2107.82,180.546 \n",
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     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(legend=:bottomright)\n",
    "plot!(p, mean(bandit_testbed(;explorer=EpsilonGreedyExplorer(0.), init=5., opt=Descent(0.1))[2] for _ in 1:2000), label=\"Q_1=5, epsilon=0.\")\n",
    "plot!(p, mean(bandit_testbed(;explorer=EpsilonGreedyExplorer(0.1), init=0., opt=Descent(0.1))[2] for _ in 1:2000), label=\"Q_1=0, epsilon=0.1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:00\u001b[39m\n"
     ]
    },
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       "  1602.25,189.248 1605.08,162.642 1607.9,208.77 1610.72,200.586 1613.55,198.547 1616.37,223.505 1619.2,207.886 1622.02,204.283 1624.85,217.648 1627.67,211.922 \n",
       "  1630.5,190.532 1633.32,224.95 1636.14,197.176 1638.97,199.977 1641.79,211.209 1644.62,183.125 1647.44,196.822 1650.27,233.801 1653.09,192.095 1655.91,194.004 \n",
       "  1658.74,205.707 1661.56,194.905 1664.39,185.269 1667.21,186.185 1670.04,199.5 1672.86,206.663 1675.69,199.992 1678.51,200.769 1681.33,207.659 1684.16,200.465 \n",
       "  1686.98,206.544 1689.81,202.623 1692.63,220.467 1695.46,186.604 1698.28,216.183 1701.1,195.929 1703.93,221.643 1706.75,206.124 1709.58,197.993 1712.4,173.628 \n",
       "  1715.23,188.719 1718.05,211.876 1720.88,224.828 1723.7,186.89 1726.52,193.614 1729.35,218.77 1732.17,217.902 1735,185.688 1737.82,162.552 1740.65,196.717 \n",
       "  1743.47,193.934 1746.3,200.638 1749.12,158.292 1751.94,186.954 1754.77,207.359 1757.59,189.163 1760.42,186.159 1763.24,197.207 1766.07,198.942 1768.89,193.634 \n",
       "  1771.71,202.305 1774.54,210.959 1777.36,186.37 1780.19,168.149 1783.01,165.111 1785.84,173.543 1788.66,180.606 1791.49,204.446 1794.31,195.048 1797.13,181.896 \n",
       "  1799.96,184.464 1802.78,179.971 1805.61,196.796 1808.43,161.012 1811.26,219.099 1814.08,192.423 1816.9,176.305 1819.73,176.216 1822.55,199.982 1825.38,201.502 \n",
       "  1828.2,190.034 1831.03,205.255 1833.85,190.277 1836.68,183.607 1839.5,192.679 1842.32,179.773 1845.15,168.774 1847.97,201.217 1850.8,188.031 1853.62,193.576 \n",
       "  1856.45,126.304 1859.27,173.743 1862.1,196.927 1864.92,197.562 1867.74,208.942 1870.57,167.363 1873.39,158.774 1876.22,220.764 1879.04,183.473 1881.87,183.139 \n",
       "  1884.69,182.012 1887.51,209.618 1890.34,174.272 1893.16,187.733 1895.99,184.309 1898.81,150.791 1901.64,194.452 1904.46,192.309 1907.29,157.956 1910.11,177.553 \n",
       "  1912.93,175.22 1915.76,201.568 1918.58,194.721 1921.41,184.996 1924.23,196.569 1927.06,190.028 1929.88,176.707 1932.7,184.424 1935.53,180.277 1938.35,151.962 \n",
       "  1941.18,181.87 1944,199.443 1946.83,186.731 1949.65,186.259 1952.48,181.047 1955.3,206.267 1958.12,178.855 1960.95,180.811 1963.77,168.467 1966.6,180.9 \n",
       "  1969.42,184.632 1972.25,172.215 1975.07,206.765 1977.9,184.433 1980.72,152.998 1983.54,176.845 1986.37,168.913 1989.19,170.235 1992.02,183.053 1994.84,156.869 \n",
       "  1997.67,153.558 2000.49,151.419 2003.31,188.022 2006.14,209.252 2008.96,194.553 2011.79,158.949 2014.61,179.638 2017.44,167.05 2020.26,185.84 2023.09,158.454 \n",
       "  2025.91,199.139 2028.73,187.983 2031.56,184.478 2034.38,202.948 2037.21,198.978 2040.03,162.642 2042.86,168.858 2045.68,169.86 2048.5,181.804 2051.33,196.782 \n",
       "  2054.15,200.347 2056.98,159.353 2059.8,165.357 2062.63,179.856 2065.45,159.382 2068.28,147.83 2071.1,161.553 2073.92,170.704 2076.75,174.704 2079.57,181.942 \n",
       "  2082.4,154.96 2085.22,158.079 2088.05,228.291 2090.87,185.316 2093.69,166.461 2096.52,180.809 2099.34,156.731 2102.17,158.073 2104.99,168.541 2107.82,174.725 \n",
       "  2110.64,160.819 2113.47,171.29 2116.29,184.961 2119.11,175.318 2121.94,160.678 2124.76,158.452 2127.59,187.516 2130.41,185.978 2133.24,158.933 2136.06,159.494 \n",
       "  2138.89,173.759 2141.71,171.99 2144.53,150.646 2147.36,151.031 2150.18,134.708 2153.01,177.724 2155.83,173.008 2158.66,192.462 2161.48,185.461 2164.3,182.841 \n",
       "  2167.13,184.489 2169.95,132.972 2172.78,166.911 2175.6,176.361 2178.43,191.003 2181.25,178.787 2184.08,161.965 2186.9,179.334 2189.72,158.098 2192.55,199.401 \n",
       "  2195.37,142.086 2198.2,171.979 2201.02,147.869 2203.85,197.952 2206.67,148.809 2209.49,155.734 2212.32,159.859 2215.14,151.94 2217.97,183.625 2220.79,179.728 \n",
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       "  2251.86,169.837 2254.69,180.501 2257.51,148.105 2260.33,189.348 2263.16,174.086 2265.98,129.564 2268.81,163.599 2271.63,137.505 2274.46,150.995 2277.28,206.075 \n",
       "  2280.1,163.935 2282.93,154.266 2285.75,156.153 2288.58,179.629 2291.4,170.176 2294.23,157.815 2297.05,216.446 2299.88,158.397 2302.7,172.545 2305.52,139.735 \n",
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       "  2336.59,150.696 2339.42,151.611 2342.24,142.251 2345.07,167.286 2347.89,167.716 2350.71,145.518 2353.54,175.362 2356.36,169.724 2359.19,181.893 2362.01,137.726 \n",
       "  2364.84,153.399 2367.66,139.131 2370.49,188.488 2373.31,139.858 2376.13,147.915 2378.96,201.893 2381.78,154.943 2384.61,169.103 2387.43,131.412 2390.26,142.336 \n",
       "  2393.08,160.515 2395.9,171.643 2398.73,128.644 2401.55,133.252 2404.38,157.54 2407.2,138.704 2410.03,150.501 2412.85,157.065 2415.68,153.303 2418.5,148.689 \n",
       "  2421.32,171.817 2424.15,153.117 2426.97,151.17 2429.8,167.772 2432.62,123.757 2435.45,159.634 2438.27,146.229 2441.09,129.094 2443.92,170.957 2446.74,118.515 \n",
       "  2449.57,170.592 2452.39,167.642 2455.22,124.753 2458.04,171.778 2460.87,157.447 2463.69,151.905 2466.51,134.35 2469.34,177.951 2472.16,178.992 2474.99,148.547 \n",
       "  2477.81,153.715 2480.64,172.987 2483.46,160.085 2486.28,156.822 2489.11,164.276 2491.93,170.908 2494.76,152.175 2497.58,152.927 2500.41,153.376 2503.23,161.727 \n",
       "  2506.06,165.484 2508.88,155.273 2511.7,174.151 2514.53,160.057 2517.35,149.83 2520.18,170.531 2523,155.4 2525.83,156.138 2528.65,125.062 2531.48,145.393 \n",
       "  2534.3,172.912 2537.12,154.985 2539.95,178.325 2542.77,188.525 2545.6,161.164 2548.42,161.668 2551.25,174.219 2554.07,159.37 2556.89,160.548 2559.72,163.192 \n",
       "  2562.54,148.195 2565.37,186.342 2568.19,161.153 2571.02,162.11 2573.84,135.4 2576.67,174.523 2579.49,134.396 2582.31,141.297 2585.14,140.006 2587.96,142.733 \n",
       "  2590.79,155.797 2593.61,147.36 2596.44,157.176 2599.26,145.56 2602.08,176.526 2604.91,166.45 2607.73,149.934 2610.56,154.594 2613.38,168.916 2616.21,160.1 \n",
       "  2619.03,143.118 2621.86,123.306 2624.68,149.434 2627.5,133.918 2630.33,175.416 2633.15,132.2 2635.98,167.502 2638.8,177.567 2641.63,126.878 2644.45,150.643 \n",
       "  2647.28,157.614 2650.1,142.84 2652.92,128.656 2655.75,173.025 2658.57,166.153 2661.4,150.454 2664.22,164.641 2667.05,124.587 2669.87,124.766 2672.69,181.217 \n",
       "  2675.52,139.151 2678.34,167.978 2681.17,135.878 2683.99,146.475 2686.82,122.984 2689.64,157.551 2692.47,155.103 2695.29,133.02 2698.11,144.501 2700.94,137.311 \n",
       "  2703.76,169.356 2706.59,159.785 2709.41,146.371 2712.24,159.883 2715.06,126.023 2717.88,137.806 2720.71,147.934 2723.53,165.605 2726.36,132.935 2729.18,156.896 \n",
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       "  1122.11,385.48 1124.93,352.911 1127.75,380.34 1130.58,342.805 1133.4,353.399 1136.23,369.151 1139.05,366.793 1141.88,358.835 1144.7,340.299 1147.52,312.714 \n",
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       "  1291.57,329.139 1294.39,330.181 1297.22,328.921 1300.04,327.382 1302.87,325.761 1305.69,320.55 1308.51,341.087 1311.34,316.37 1314.16,323.013 1316.99,346.515 \n",
       "  1319.81,339.253 1322.64,317.989 1325.46,321.598 1328.29,320.591 1331.11,312.433 1333.93,335.556 1336.76,300.682 1339.58,296.254 1342.41,318.094 1345.23,320.874 \n",
       "  1348.06,309.18 1350.88,350.058 1353.71,292.784 1356.53,348.765 1359.35,322.695 1362.18,332.918 1365,316.263 1367.83,319.091 1370.65,316.777 1373.48,333.94 \n",
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       "  1461.03,290.138 1463.86,255.031 1466.68,303.987 1469.51,320.058 1472.33,304.77 1475.15,301.457 1477.98,330.67 1480.8,300.09 1483.63,292.429 1486.45,307.699 \n",
       "  1489.28,312.95 1492.1,268.528 1494.92,296.161 1497.75,327.893 1500.57,283.535 1503.4,334.913 1506.22,270.607 1509.05,305.247 1511.87,324.53 1514.7,303.68 \n",
       "  1517.52,313.171 1520.34,327.231 1523.17,321.586 1525.99,281.459 1528.82,324.407 1531.64,313.259 1534.47,297.914 1537.29,308.531 1540.11,335.069 1542.94,306.96 \n",
       "  1545.76,294.359 1548.59,259.244 1551.41,295.434 1554.24,281.991 1557.06,303.326 1559.89,341.867 1562.71,293.538 1565.53,319.584 1568.36,278.8 1571.18,261.753 \n",
       "  1574.01,278.007 1576.83,288.818 1579.66,316.838 1582.48,272.998 1585.31,300.401 1588.13,288.853 1590.95,317.387 1593.78,299.752 1596.6,270.366 1599.43,277.328 \n",
       "  1602.25,291.814 1605.08,265.539 1607.9,264.256 1610.72,299.056 1613.55,313.5 1616.37,253.102 1619.2,312.63 1622.02,312.661 1624.85,284.498 1627.67,263.912 \n",
       "  1630.5,289.013 1633.32,282.844 1636.14,284.866 1638.97,294.689 1641.79,294.764 1644.62,280.071 1647.44,225.127 1650.27,309.693 1653.09,275.636 1655.91,303.584 \n",
       "  1658.74,283.936 1661.56,266.049 1664.39,287.406 1667.21,293.147 1670.04,251.871 1672.86,287.667 1675.69,306.685 1678.51,261.135 1681.33,300.225 1684.16,283.268 \n",
       "  1686.98,252.127 1689.81,290.49 1692.63,276.143 1695.46,281.104 1698.28,272.421 1701.1,298.449 1703.93,259.149 1706.75,291.48 1709.58,280.176 1712.4,276.873 \n",
       "  1715.23,302.872 1718.05,281.184 1720.88,274.92 1723.7,309.169 1726.52,303.379 1729.35,295.849 1732.17,299.791 1735,263.38 1737.82,278.649 1740.65,302.918 \n",
       "  1743.47,262.668 1746.3,278.173 1749.12,296.858 1751.94,296.879 1754.77,271.484 1757.59,284.941 1760.42,264.895 1763.24,260.372 1766.07,276.095 1768.89,294.773 \n",
       "  1771.71,272.841 1774.54,298.123 1777.36,275.944 1780.19,285.678 1783.01,244.87 1785.84,272.662 1788.66,272.475 1791.49,263.238 1794.31,283.458 1797.13,288.931 \n",
       "  1799.96,261.367 1802.78,276.254 1805.61,298.706 1808.43,269.616 1811.26,293.327 1814.08,272.919 1816.9,252.922 1819.73,275.967 1822.55,247.653 1825.38,276.582 \n",
       "  1828.2,299.69 1831.03,256.842 1833.85,263.185 1836.68,303.77 1839.5,260.267 1842.32,310.893 1845.15,261.158 1847.97,248.731 1850.8,281.21 1853.62,291.003 \n",
       "  1856.45,249.515 1859.27,274.968 1862.1,237.732 1864.92,279.932 1867.74,315.287 1870.57,243.191 1873.39,281.004 1876.22,267.977 1879.04,274.513 1881.87,279.881 \n",
       "  1884.69,236.313 1887.51,281.298 1890.34,269.477 1893.16,304.29 1895.99,251.284 1898.81,272.837 1901.64,302.22 1904.46,267.172 1907.29,249.814 1910.11,275.234 \n",
       "  1912.93,277.643 1915.76,275.515 1918.58,306.522 1921.41,285.925 1924.23,296.238 1927.06,279.241 1929.88,271.172 1932.7,282.46 1935.53,278.257 1938.35,243.934 \n",
       "  1941.18,264.047 1944,260.753 1946.83,267.819 1949.65,253.884 1952.48,290.561 1955.3,273.302 1958.12,257.612 1960.95,288.887 1963.77,275.45 1966.6,270.929 \n",
       "  1969.42,267.057 1972.25,265.695 1975.07,281.568 1977.9,236.037 1980.72,269.903 1983.54,253.903 1986.37,245.336 1989.19,231.335 1992.02,256.502 1994.84,247.669 \n",
       "  1997.67,282.415 2000.49,253.073 2003.31,247.295 2006.14,268.86 2008.96,260.581 2011.79,275.996 2014.61,280.195 2017.44,255.207 2020.26,250.476 2023.09,235.459 \n",
       "  2025.91,236.702 2028.73,269.003 2031.56,274.576 2034.38,276.802 2037.21,269.055 2040.03,237.315 2042.86,283.073 2045.68,253.502 2048.5,246.33 2051.33,240.727 \n",
       "  2054.15,251.208 2056.98,227.838 2059.8,238.928 2062.63,264.249 2065.45,227.533 2068.28,253.127 2071.1,242.501 2073.92,245.786 2076.75,248.849 2079.57,226.7 \n",
       "  2082.4,245.998 2085.22,237.45 2088.05,244.334 2090.87,258.136 2093.69,244.344 2096.52,261.437 2099.34,238.729 2102.17,268.01 2104.99,279.469 2107.82,249.446 \n",
       "  2110.64,255.059 2113.47,267.46 2116.29,266.839 2119.11,260.881 2121.94,249.835 2124.76,272.268 2127.59,245.658 2130.41,233.583 2133.24,267.443 2136.06,271.866 \n",
       "  2138.89,276.942 2141.71,259.21 2144.53,252.362 2147.36,225.234 2150.18,216.544 2153.01,252.064 2155.83,219.943 2158.66,263.347 2161.48,226.045 2164.3,250.761 \n",
       "  2167.13,232.67 2169.95,254.466 2172.78,231.136 2175.6,245.171 2178.43,237.546 2181.25,255.765 2184.08,240.939 2186.9,226.26 2189.72,235.486 2192.55,269.782 \n",
       "  2195.37,256.005 2198.2,257.715 2201.02,287.707 2203.85,263.356 2206.67,263.705 2209.49,279.048 2212.32,238.91 2215.14,252.121 2217.97,239.181 2220.79,236.012 \n",
       "  2223.62,241.439 2226.44,249.295 2229.27,238.801 2232.09,272.513 2234.91,239.859 2237.74,252.221 2240.56,221.157 2243.39,208.811 2246.21,316.173 2249.04,258.304 \n",
       "  2251.86,275.775 2254.69,255.273 2257.51,233.944 2260.33,235.522 2263.16,226.541 2265.98,250.471 2268.81,223.517 2271.63,210.688 2274.46,206.651 2277.28,236.186 \n",
       "  2280.1,224.271 2282.93,230.467 2285.75,258.159 2288.58,244.882 2291.4,276.717 2294.23,241.979 2297.05,243.65 2299.88,251.555 2302.7,241.619 2305.52,262.28 \n",
       "  2308.35,268.424 2311.17,240.741 2314,244.803 2316.82,233.465 2319.65,260.885 2322.47,203.979 2325.29,228.627 2328.12,248.904 2330.94,256.341 2333.77,227.193 \n",
       "  2336.59,243.395 2339.42,268.484 2342.24,256.56 2345.07,261.934 2347.89,214.903 2350.71,245.945 2353.54,249.8 2356.36,253.438 2359.19,231.675 2362.01,212.903 \n",
       "  2364.84,227.815 2367.66,244.869 2370.49,230.777 2373.31,262.518 2376.13,230.569 2378.96,245.759 2381.78,221.706 2384.61,250.685 2387.43,234.706 2390.26,204.288 \n",
       "  2393.08,259.842 2395.9,244.931 2398.73,205.811 2401.55,267.203 2404.38,232.795 2407.2,280.887 2410.03,244.579 2412.85,266.683 2415.68,242.289 2418.5,257.116 \n",
       "  2421.32,216.113 2424.15,262.17 2426.97,272.709 2429.8,261.036 2432.62,254.022 2435.45,239.077 2438.27,250.704 2441.09,185.722 2443.92,230.903 2446.74,214.602 \n",
       "  2449.57,269.084 2452.39,265.843 2455.22,234.811 2458.04,211.182 2460.87,263.844 2463.69,269.485 2466.51,251.323 2469.34,256.18 2472.16,236.348 2474.99,241.605 \n",
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      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(legend=:bottomright)\n",
    "plot!(p, mean(bandit_testbed(;explorer=UCBExplorer(10), opt=Descent(0.1))[1] for _ in 1:5000), label=\"UpperConfidenceBound, c=2\")\n",
    "plot!(p, mean(bandit_testbed(;explorer=EpsilonGreedyExplorer(0.1), opt=Descent(0.1))[1] for _ in 1:5000), label=\"epsilon-greedy, epsilon=0.1\")\n",
    "\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gb_bandit_testbed (generic function with 1 method)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gb_bandit_testbed(;baseline=0., explorer=WeightedExplorer(is_normalized=true), truereward=0.0, init=0., opt=InvDecay(1.0))\n",
    "    env = MultiArmBanditsEnv(truereward=truereward)\n",
    "    agent = Agent(\n",
    "        policy=QBasedPolicy(\n",
    "            learner=GradientBanditLearner(\n",
    "                approximator=TabularApproximator(\n",
    "                    n_state=length(get_observation_space(env)),\n",
    "                    n_action=length(get_action_space(env)),\n",
    "                    init=init\n",
    "                ),\n",
    "                optimizer=opt,\n",
    "                baseline=baseline\n",
    "            ),\n",
    "            explorer=explorer\n",
    "        ),\n",
    "        trajectory=EpisodicCompactSARTSATrajectory()\n",
    "    )\n",
    "    best_action_stats, reward_stats = CollectBestActions(), RewardsPerEpisode()\n",
    "    run(agent, env, StopAfterStep(1000), ComposedHook(best_action_stats, reward_stats))\n",
    "    collect(Iterators.flatten(reward_stats.rewards)),best_action_stats.isbest\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the only difference of `gb_bandit_testbed` compared to `bandit_testbed` is that it uses `GradientBanditLearner` instread of `TDLearner`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:00\u001b[39m\n",
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:00\u001b[39m\n"
     ]
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       "  698.447,695.387 701.271,717.311 704.096,713.2 706.92,722.792 709.745,713.2 712.569,681.685 715.393,733.754 718.218,694.017 721.042,683.055 723.867,652.91 \n",
       "  726.691,669.353 729.515,698.128 732.34,636.468 735.164,661.132 737.988,665.243 740.813,596.731 743.637,652.91 746.462,630.987 749.286,637.838 752.11,647.43 \n",
       "  754.935,672.094 757.759,635.098 760.584,639.208 763.408,615.914 766.232,620.025 769.057,629.617 771.881,598.102 774.706,602.212 777.53,628.246 780.354,598.102 \n",
       "  783.179,593.991 786.003,622.766 788.827,561.105 791.652,584.399 794.476,569.327 797.301,602.212 800.125,595.361 802.949,561.105 805.774,615.914 808.598,576.178 \n",
       "  811.423,603.582 814.247,574.808 817.071,550.144 819.896,573.438 822.72,552.884 825.545,572.067 828.369,543.293 831.193,572.067 834.018,555.625 836.842,515.888 \n",
       "  839.666,532.331 842.491,547.403 845.315,548.773 848.14,517.258 850.964,546.033 853.788,496.705 856.613,491.224 859.437,504.926 862.262,537.812 865.086,552.884 \n",
       "  867.91,481.632 870.735,525.48 873.559,513.148 876.384,485.743 879.208,513.148 882.032,477.522 884.857,493.965 887.681,509.037 890.505,477.522 893.33,480.262 \n",
       "  896.154,502.186 898.979,483.003 901.803,492.594 904.627,495.335 907.452,504.926 910.276,509.037 913.101,483.003 915.925,477.522 918.749,452.858 921.574,455.598 \n",
       "  924.398,444.636 927.223,450.117 930.047,461.079 932.871,472.041 935.696,476.152 938.52,483.003 941.344,481.632 944.169,504.926 946.993,450.117 949.818,428.194 \n",
       "  952.642,440.526 955.466,447.377 958.291,419.972 961.115,446.007 963.94,456.968 966.764,447.377 969.588,450.117 972.413,435.045 975.237,433.675 978.062,450.117 \n",
       "  980.886,419.972 983.71,463.82 986.535,432.304 989.359,413.121 992.183,433.675 995.008,430.934 997.832,436.415 1000.66,417.232 1003.48,391.198 1006.31,389.827 \n",
       "  1009.13,407.64 1011.95,395.308 1014.78,429.564 1017.6,414.492 1020.43,432.304 1023.25,430.934 1026.08,382.976 1028.9,370.644 1031.72,409.011 1034.55,392.568 \n",
       "  1037.37,392.568 1040.2,395.308 1043.02,396.679 1045.85,391.198 1048.67,396.679 1051.5,400.789 1054.32,419.972 1057.14,395.308 1059.97,370.644 1062.79,366.534 \n",
       "  1065.62,414.492 1068.44,391.198 1071.27,414.492 1074.09,355.572 1076.92,380.236 1079.74,372.015 1082.56,372.015 1085.39,350.091 1088.21,367.904 1091.04,400.789 \n",
       "  1093.86,352.831 1096.69,365.163 1099.51,363.793 1102.33,337.759 1105.16,370.644 1107.98,372.015 1110.81,374.755 1113.63,341.87 1116.46,367.904 1119.28,336.389 \n",
       "  1122.11,362.423 1124.93,355.572 1127.75,367.904 1130.58,359.683 1133.4,373.385 1136.23,362.423 1139.05,363.793 1141.88,351.461 1144.7,361.053 1147.52,369.274 \n",
       "  1150.35,362.423 1153.17,350.091 1156,352.831 1158.82,369.274 1161.65,359.683 1164.47,352.831 1167.3,339.129 1170.12,363.793 1172.94,324.057 1175.77,361.053 \n",
       "  1178.59,325.427 1181.42,328.167 1184.24,363.793 1187.07,348.721 1189.89,329.538 1192.72,333.648 1195.54,359.683 1198.36,354.202 1201.19,314.465 1204.01,321.316 \n",
       "  1206.84,325.427 1209.66,337.759 1212.49,344.61 1215.31,306.244 1218.13,311.725 1220.96,335.019 1223.78,333.648 1226.61,335.019 1229.43,339.129 1232.26,315.835 \n",
       "  1235.08,315.835 1237.91,351.461 1240.73,311.725 1243.55,335.019 1246.38,339.129 1249.2,317.206 1252.03,319.946 1254.85,314.465 1257.68,299.393 1260.5,328.167 \n",
       "  1263.32,313.095 1266.15,325.427 1268.97,291.171 1271.8,311.725 1274.62,298.022 1277.45,321.316 1280.27,300.763 1283.1,317.206 1285.92,291.171 1288.74,295.282 \n",
       "  1291.57,302.133 1294.39,298.022 1297.22,295.282 1300.04,281.58 1302.87,307.614 1305.69,292.542 1308.51,277.469 1311.34,314.465 1314.16,319.946 1316.99,284.32 \n",
       "  1319.81,266.507 1322.64,298.022 1325.46,319.946 1328.29,292.542 1331.11,292.542 1333.93,307.614 1336.76,302.133 1339.58,311.725 1342.41,285.69 1345.23,308.984 \n",
       "  1348.06,293.912 1350.88,278.839 1353.71,282.95 1356.53,284.32 1359.35,287.061 1362.18,296.652 1365,285.69 1367.83,303.503 1370.65,293.912 1373.48,269.248 \n",
       "  1376.3,284.32 1379.12,291.171 1381.95,282.95 1384.77,271.988 1387.6,292.542 1390.42,273.358 1393.25,285.69 1396.07,291.171 1398.9,276.099 1401.72,273.358 \n",
       "  1404.54,266.507 1407.37,271.988 1410.19,261.026 1413.02,289.801 1415.84,284.32 1418.67,263.767 1421.49,288.431 1424.31,266.507 1427.14,278.839 1429.96,277.469 \n",
       "  1432.79,270.618 1435.61,277.469 1438.44,263.767 1441.26,271.988 1444.09,261.026 1446.91,265.137 1449.73,255.546 1452.56,269.248 1455.38,259.656 1458.21,256.916 \n",
       "  1461.03,262.397 1463.86,271.988 1466.68,274.729 1469.51,273.358 1472.33,247.324 1475.15,273.358 1477.98,295.282 1480.8,248.694 1483.63,245.954 1486.45,263.767 \n",
       "  1489.28,263.767 1492.1,245.954 1494.92,259.656 1497.75,244.584 1500.57,247.324 1503.4,256.916 1506.22,256.916 1509.05,245.954 1511.87,244.584 1514.7,270.618 \n",
       "  1517.52,255.546 1520.34,256.916 1523.17,255.546 1525.99,258.286 1528.82,244.584 1531.64,255.546 1534.47,256.916 1537.29,244.584 1540.11,241.843 1542.94,267.878 \n",
       "  1545.76,259.656 1548.59,247.324 1551.41,256.916 1554.24,269.248 1557.06,259.656 1559.89,244.584 1562.71,254.175 1565.53,254.175 1568.36,262.397 1571.18,248.694 \n",
       "  1574.01,239.103 1576.83,269.248 1579.66,244.584 1582.48,237.733 1585.31,245.954 1588.13,218.549 1590.95,233.622 1593.78,244.584 1596.6,244.584 1599.43,247.324 \n",
       "  1602.25,258.286 1605.08,240.473 1607.9,244.584 1610.72,237.733 1613.55,230.882 1616.37,243.214 1619.2,237.733 1622.02,244.584 1624.85,244.584 1627.67,221.29 \n",
       "  1630.5,224.03 1633.32,222.66 1636.14,252.805 1638.97,221.29 1641.79,221.29 1644.62,247.324 1647.44,236.362 1650.27,230.882 1653.09,229.511 1655.91,225.401 \n",
       "  1658.74,234.992 1661.56,233.622 1664.39,251.435 1667.21,213.069 1670.04,229.511 1672.86,218.549 1675.69,237.733 1678.51,243.214 1681.33,250.065 1684.16,251.435 \n",
       "  1686.98,213.069 1689.81,236.362 1692.63,230.882 1695.46,221.29 1698.28,217.179 1701.1,232.252 1703.93,214.439 1706.75,228.141 1709.58,234.992 1712.4,230.882 \n",
       "  1715.23,204.847 1718.05,219.92 1720.88,226.771 1723.7,221.29 1726.52,236.362 1729.35,250.065 1732.17,247.324 1735,222.66 1737.82,226.771 1740.65,221.29 \n",
       "  1743.47,240.473 1746.3,250.065 1749.12,224.03 1751.94,219.92 1754.77,240.473 1757.59,219.92 1760.42,224.03 1763.24,225.401 1766.07,230.882 1768.89,207.588 \n",
       "  1771.71,240.473 1774.54,222.66 1777.36,233.622 1780.19,206.217 1783.01,218.549 1785.84,210.328 1788.66,210.328 1791.49,228.141 1794.31,204.847 1797.13,233.622 \n",
       "  1799.96,204.847 1802.78,219.92 1805.61,203.477 1808.43,192.515 1811.26,199.366 1814.08,200.737 1816.9,199.366 1819.73,226.771 1822.55,206.217 1825.38,208.958 \n",
       "  1828.2,213.069 1831.03,208.958 1833.85,192.515 1836.68,206.217 1839.5,204.847 1842.32,214.439 1845.15,207.588 1847.97,207.588 1850.8,207.588 1853.62,207.588 \n",
       "  1856.45,200.737 1859.27,207.588 1862.1,218.549 1864.92,189.775 1867.74,196.626 1870.57,210.328 1873.39,208.958 1876.22,191.145 1879.04,204.847 1881.87,210.328 \n",
       "  1884.69,202.107 1887.51,202.107 1890.34,202.107 1893.16,199.366 1895.99,196.626 1898.81,197.996 1901.64,213.069 1904.46,207.588 1907.29,176.073 1910.11,196.626 \n",
       "  1912.93,214.439 1915.76,203.477 1918.58,191.145 1921.41,177.443 1924.23,213.069 1927.06,200.737 1929.88,211.698 1932.7,203.477 1935.53,196.626 1938.35,200.737 \n",
       "  1941.18,191.145 1944,219.92 1946.83,188.405 1949.65,196.626 1952.48,196.626 1955.3,192.515 1958.12,202.107 1960.95,196.626 1963.77,210.328 1966.6,189.775 \n",
       "  1969.42,193.885 1972.25,196.626 1975.07,204.847 1977.9,214.439 1980.72,192.515 1983.54,213.069 1986.37,184.294 1989.19,196.626 1992.02,200.737 1994.84,166.481 \n",
       "  1997.67,188.405 2000.49,197.996 2003.31,177.443 2006.14,195.256 2008.96,182.924 2011.79,195.256 2014.61,196.626 2017.44,195.256 2020.26,180.183 2023.09,195.256 \n",
       "  2025.91,189.775 2028.73,169.221 2031.56,195.256 2034.38,177.443 2037.21,189.775 2040.03,202.107 2042.86,206.217 2045.68,176.073 2048.5,188.405 2051.33,191.145 \n",
       "  2054.15,208.958 2056.98,174.702 2059.8,181.553 2062.63,185.664 2065.45,193.885 2068.28,178.813 2071.1,185.664 2073.92,195.256 2076.75,189.775 2079.57,188.405 \n",
       "  2082.4,174.702 2085.22,181.553 2088.05,182.924 2090.87,178.813 2093.69,197.996 2096.52,165.111 2099.34,197.996 2102.17,181.553 2104.99,185.664 2107.82,177.443 \n",
       "  2110.64,188.405 2113.47,177.443 2116.29,177.443 2119.11,189.775 2121.94,169.221 2124.76,184.294 2127.59,187.034 2130.41,182.924 2133.24,185.664 2136.06,193.885 \n",
       "  2138.89,200.737 2141.71,182.924 2144.53,170.592 2147.36,181.553 2150.18,185.664 2153.01,184.294 2155.83,176.073 2158.66,176.073 2161.48,180.183 2164.3,189.775 \n",
       "  2167.13,170.592 2169.95,180.183 2172.78,173.332 2175.6,176.073 2178.43,181.553 2181.25,180.183 2184.08,171.962 2186.9,174.702 2189.72,180.183 2192.55,177.443 \n",
       "  2195.37,163.741 2198.2,195.256 2201.02,182.924 2203.85,174.702 2206.67,188.405 2209.49,173.332 2212.32,176.073 2215.14,185.664 2217.97,184.294 2220.79,189.775 \n",
       "  2223.62,158.26 2226.44,173.332 2229.27,166.481 2232.09,187.034 2234.91,177.443 2237.74,195.256 2240.56,167.851 2243.39,152.779 2246.21,200.737 2249.04,173.332 \n",
       "  2251.86,182.924 2254.69,181.553 2257.51,178.813 2260.33,191.145 2263.16,169.221 2265.98,171.962 2268.81,182.924 2271.63,173.332 2274.46,180.183 2277.28,177.443 \n",
       "  2280.1,177.443 2282.93,176.073 2285.75,167.851 2288.58,158.26 2291.4,181.553 2294.23,166.481 2297.05,165.111 2299.88,159.63 2302.7,170.592 2305.52,195.256 \n",
       "  2308.35,167.851 2311.17,169.221 2314,187.034 2316.82,161 2319.65,167.851 2322.47,177.443 2325.29,163.741 2328.12,182.924 2330.94,169.221 2333.77,155.519 \n",
       "  2336.59,156.889 2339.42,176.073 2342.24,177.443 2345.07,156.889 2347.89,178.813 2350.71,174.702 2353.54,177.443 2356.36,165.111 2359.19,171.962 2362.01,156.889 \n",
       "  2364.84,162.37 2367.66,166.481 2370.49,159.63 2373.31,155.519 2376.13,170.592 2378.96,162.37 2381.78,162.37 2384.61,166.481 2387.43,193.885 2390.26,178.813 \n",
       "  2393.08,171.962 2395.9,159.63 2398.73,165.111 2401.55,152.779 2404.38,148.668 2407.2,159.63 2410.03,158.26 2412.85,163.741 2415.68,152.779 2418.5,165.111 \n",
       "  2421.32,150.038 2424.15,173.332 2426.97,161 2429.8,170.592 2432.62,163.741 2435.45,173.332 2438.27,170.592 2441.09,162.37 2443.92,170.592 2446.74,173.332 \n",
       "  2449.57,156.889 2452.39,162.37 2455.22,152.779 2458.04,159.63 2460.87,169.221 2463.69,171.962 2466.51,166.481 2469.34,148.668 2472.16,161 2474.99,159.63 \n",
       "  2477.81,133.596 2480.64,169.221 2483.46,159.63 2486.28,174.702 2489.11,169.221 2491.93,159.63 2494.76,181.553 2497.58,162.37 2500.41,162.37 2503.23,156.889 \n",
       "  2506.06,155.519 2508.88,167.851 2511.7,145.928 2514.53,163.741 2517.35,156.889 2520.18,165.111 2523,167.851 2525.83,163.741 2528.65,158.26 2531.48,140.447 \n",
       "  2534.3,173.332 2537.12,147.298 2539.95,158.26 2542.77,165.111 2545.6,156.889 2548.42,161 2551.25,162.37 2554.07,148.668 2556.89,171.962 2559.72,156.889 \n",
       "  2562.54,150.038 2565.37,162.37 2568.19,144.557 2571.02,162.37 2573.84,165.111 2576.67,152.779 2579.49,165.111 2582.31,163.741 2585.14,169.221 2587.96,174.702 \n",
       "  2590.79,169.221 2593.61,147.298 2596.44,140.447 2599.26,156.889 2602.08,152.779 2604.91,159.63 2607.73,148.668 2610.56,156.889 2613.38,158.26 2616.21,167.851 \n",
       "  2619.03,136.336 2621.86,136.336 2624.68,167.851 2627.5,158.26 2630.33,148.668 2633.15,173.332 2635.98,141.817 2638.8,155.519 2641.63,145.928 2644.45,147.298 \n",
       "  2647.28,154.149 2650.1,151.409 2652.92,165.111 2655.75,162.37 2658.57,163.741 2661.4,158.26 2664.22,165.111 2667.05,150.038 2669.87,158.26 2672.69,162.37 \n",
       "  2675.52,148.668 2678.34,150.038 2681.17,154.149 2683.99,133.596 2686.82,143.187 2689.64,145.928 2692.47,152.779 2695.29,148.668 2698.11,158.26 2700.94,143.187 \n",
       "  2703.76,159.63 2706.59,162.37 2709.41,151.409 2712.24,147.298 2715.06,151.409 2717.88,156.889 2720.71,158.26 2723.53,137.706 2726.36,137.706 2729.18,139.077 \n",
       "  2732.01,159.63 2734.83,147.298 2737.66,154.149 2740.48,147.298 2743.3,151.409 2746.13,152.779 2748.95,145.928 2751.78,137.706 2754.6,137.706 2757.43,144.557 \n",
       "  2760.25,136.336 2763.08,136.336 2765.9,148.668 2768.72,145.928 2771.55,152.779 2774.37,147.298 2777.2,133.596 2780.02,136.336 2782.85,151.409 2785.67,154.149 \n",
       "  2788.49,148.668 2791.32,158.26 2794.14,150.038 2796.97,137.706 2799.79,159.63 2802.62,144.557 2805.44,154.149 2808.27,143.187 2811.09,143.187 2813.91,155.519 \n",
       "  2816.74,143.187 2819.56,163.741 2822.39,145.928 2825.21,145.928 2828.04,136.336 2830.86,137.706 2833.68,129.485 2836.51,145.928 2839.33,140.447 2842.16,155.519 \n",
       "  2844.98,134.966 2847.81,141.817 2850.63,144.557 2853.46,148.668 2856.28,147.298 2859.1,136.336 2861.93,139.077 2864.75,136.336 2867.58,140.447 2870.4,148.668 \n",
       "  2873.23,140.447 2876.05,144.557 2878.87,144.557 2881.7,136.336 2884.52,143.187 2887.35,152.779 2890.17,136.336 2893,134.966 2895.82,151.409 2898.65,144.557 \n",
       "  2901.47,122.634 2904.29,141.817 2907.12,139.077 2909.94,132.225 2912.77,141.817 2915.59,128.115 2918.42,152.779 2921.24,134.966 2924.07,137.706 2926.89,133.596 \n",
       "  2929.71,152.779 2932.54,147.298 2935.36,140.447 2938.19,133.596 2941.01,150.038 2943.84,148.668 2946.66,134.966 2949.48,136.336 2952.31,145.928 2955.13,141.817 \n",
       "  2957.96,137.706 2960.78,140.447 2963.61,152.779 2966.43,145.928 2969.26,137.706 2972.08,134.966 2974.9,140.447 2977.73,144.557 2980.55,143.187 2983.38,129.485 \n",
       "  2986.2,115.783 2989.03,140.447 2991.85,126.744 2994.67,133.596 2997.5,141.817 3000.32,110.302 3003.15,134.966 3005.97,139.077 3008.8,140.447 3011.62,141.817 \n",
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       "  3042.69,130.855 3045.51,118.523 3048.34,122.634 3051.16,144.557 3053.99,118.523 3056.81,122.634 3059.64,139.077 3062.46,133.596 3065.28,134.966 3068.11,132.225 \n",
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       "  274.789,1976.55 277.613,1929.96 280.438,1910.78 283.262,1865.56 286.086,1835.41 288.911,1823.08 291.735,1734.02 294.56,1723.06 297.384,1658.65 300.208,1605.22 \n",
       "  303.033,1594.25 305.857,1544.93 308.681,1538.08 311.506,1486.01 314.33,1487.38 317.155,1433.94 319.979,1420.24 322.803,1409.27 325.628,1362.69 328.452,1332.54 \n",
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       "  359.52,1095.49 362.345,1098.23 365.169,1096.86 367.994,1079.05 370.818,1096.86 373.642,1079.05 376.467,1018.76 379.291,1024.24 382.116,1026.98 384.94,1036.57 \n",
       "  387.764,1007.8 390.589,969.432 393.413,974.913 396.237,999.577 399.062,962.581 401.886,925.585 404.711,959.841 407.535,903.661 410.359,914.623 413.184,931.066 \n",
       "  416.008,918.734 418.833,902.291 421.657,873.517 424.481,915.993 427.306,920.104 430.13,896.81 432.955,868.036 435.779,859.814 438.603,869.406 441.428,873.517 \n",
       "  444.252,861.185 447.076,876.257 449.901,878.997 452.725,881.738 455.55,839.261 458.374,833.78 461.198,872.146 464.023,796.784 466.847,803.635 469.672,824.188 \n",
       "  472.496,820.078 475.32,813.227 478.145,792.673 480.969,795.414 483.794,806.376 486.618,789.933 489.442,772.12 492.267,777.601 495.091,777.601 497.915,776.231 \n",
       "  500.74,748.826 503.564,752.937 506.389,739.235 509.213,741.975 512.037,752.937 514.862,752.937 517.686,754.307 520.511,732.383 523.335,747.456 526.159,728.273 \n",
       "  528.984,755.677 531.808,735.124 534.633,725.532 537.457,722.792 540.281,733.754 543.106,741.975 545.93,739.235 548.754,713.2 551.579,735.124 554.403,717.311 \n",
       "  557.228,722.792 560.052,722.792 562.876,732.383 565.701,713.2 568.525,702.239 571.35,713.2 574.174,718.681 576.998,699.498 579.823,721.422 582.647,713.2 \n",
       "  585.472,702.239 588.296,711.83 591.12,709.09 593.945,685.796 596.769,688.536 599.593,714.571 602.418,706.349 605.242,673.464 608.067,704.979 610.891,694.017 \n",
       "  613.715,695.387 616.54,674.834 619.364,681.685 622.189,684.426 625.013,681.685 627.837,677.575 630.662,683.055 633.486,672.094 636.311,683.055 639.135,674.834 \n",
       "  641.959,680.315 644.784,676.204 647.608,666.613 650.432,657.021 653.257,654.281 656.081,663.872 658.906,646.059 661.73,632.357 664.554,650.17 667.379,666.613 \n",
       "  670.203,644.689 673.028,646.059 675.852,650.17 678.676,640.578 681.501,657.021 684.325,629.617 687.149,647.43 689.974,635.098 692.798,652.91 695.623,648.8 \n",
       "  698.447,654.281 701.271,641.949 704.096,636.468 706.92,628.246 709.745,621.395 712.569,637.838 715.393,632.357 718.218,632.357 721.042,637.838 723.867,639.208 \n",
       "  726.691,643.319 729.515,635.098 732.34,633.727 735.164,614.544 737.988,617.285 740.813,615.914 743.637,622.766 746.462,624.136 749.286,625.506 752.11,622.766 \n",
       "  754.935,624.136 757.759,607.693 760.584,614.544 763.408,607.693 766.232,610.434 769.057,607.693 771.881,621.395 774.706,617.285 777.53,596.731 780.354,609.063 \n",
       "  783.179,603.582 786.003,593.991 788.827,602.212 791.652,595.361 794.476,603.582 797.301,603.582 800.125,595.361 802.949,589.88 805.774,592.621 808.598,591.25 \n",
       "  811.423,604.953 814.247,603.582 817.071,613.174 819.896,592.621 822.72,589.88 825.545,591.25 828.369,604.953 831.193,587.14 834.018,591.25 836.842,599.472 \n",
       "  839.666,589.88 842.491,598.102 845.315,585.77 848.14,585.77 850.964,591.25 853.788,595.361 856.613,587.14 859.437,591.25 862.262,600.842 865.086,585.77 \n",
       "  867.91,576.178 870.735,580.289 873.559,587.14 876.384,588.51 879.208,566.586 882.032,588.51 884.857,577.548 887.681,576.178 890.505,578.918 893.33,567.957 \n",
       "  896.154,588.51 898.979,572.067 901.803,555.625 904.627,580.289 907.452,578.918 910.276,585.77 913.101,580.289 915.925,566.586 918.749,572.067 921.574,569.327 \n",
       "  924.398,566.586 927.223,574.808 930.047,565.216 932.871,563.846 935.696,570.697 938.52,570.697 941.344,561.105 944.169,580.289 946.993,567.957 949.818,559.735 \n",
       "  952.642,567.957 955.466,565.216 958.291,561.105 961.115,567.957 963.94,552.884 966.764,565.216 969.588,552.884 972.413,543.293 975.237,558.365 978.062,559.735 \n",
       "  980.886,547.403 983.71,552.884 986.535,543.293 989.359,544.663 992.183,555.625 995.008,550.144 997.832,551.514 1000.66,550.144 1003.48,539.182 1006.31,563.846 \n",
       "  1009.13,544.663 1011.95,555.625 1014.78,547.403 1017.6,539.182 1020.43,550.144 1023.25,546.033 1026.08,550.144 1028.9,550.144 1031.72,541.922 1034.55,548.773 \n",
       "  1037.37,533.701 1040.2,533.701 1043.02,551.514 1045.85,546.033 1048.67,540.552 1051.5,546.033 1054.32,541.922 1057.14,539.182 1059.97,547.403 1062.79,541.922 \n",
       "  1065.62,541.922 1068.44,541.922 1071.27,525.48 1074.09,543.293 1076.92,546.033 1079.74,541.922 1082.56,533.701 1085.39,536.441 1088.21,528.22 1091.04,532.331 \n",
       "  1093.86,536.441 1096.69,528.22 1099.51,526.85 1102.33,541.922 1105.16,536.441 1107.98,526.85 1110.81,532.331 1113.63,524.109 1116.46,526.85 1119.28,530.961 \n",
       "  1122.11,524.109 1124.93,532.331 1127.75,537.812 1130.58,540.552 1133.4,524.109 1136.23,529.59 1139.05,521.369 1141.88,529.59 1144.7,524.109 1147.52,529.59 \n",
       "  1150.35,524.109 1153.17,533.701 1156,535.071 1158.82,528.22 1161.65,529.59 1164.47,530.961 1167.3,513.148 1170.12,519.999 1172.94,519.999 1175.77,517.258 \n",
       "  1178.59,511.777 1181.42,518.629 1184.24,517.258 1187.07,518.629 1189.89,522.739 1192.72,521.369 1195.54,515.888 1198.36,511.777 1201.19,515.888 1204.01,518.629 \n",
       "  1206.84,506.297 1209.66,510.407 1212.49,525.48 1215.31,506.297 1218.13,519.999 1220.96,511.777 1223.78,515.888 1226.61,519.999 1229.43,514.518 1232.26,507.667 \n",
       "  1235.08,518.629 1237.91,509.037 1240.73,503.556 1243.55,509.037 1246.38,513.148 1249.2,506.297 1252.03,513.148 1254.85,513.148 1257.68,514.518 1260.5,509.037 \n",
       "  1263.32,500.816 1266.15,513.148 1268.97,509.037 1271.8,506.297 1274.62,506.297 1277.45,513.148 1280.27,511.777 1283.1,506.297 1285.92,503.556 1288.74,502.186 \n",
       "  1291.57,515.888 1294.39,517.258 1297.22,514.518 1300.04,519.999 1302.87,509.037 1305.69,503.556 1308.51,509.037 1311.34,509.037 1314.16,515.888 1316.99,510.407 \n",
       "  1319.81,502.186 1322.64,503.556 1325.46,503.556 1328.29,509.037 1331.11,503.556 1333.93,507.667 1336.76,510.407 1339.58,519.999 1342.41,500.816 1345.23,504.926 \n",
       "  1348.06,507.667 1350.88,499.445 1353.71,504.926 1356.53,498.075 1359.35,500.816 1362.18,503.556 1365,502.186 1367.83,492.594 1370.65,507.667 1373.48,507.667 \n",
       "  1376.3,504.926 1379.12,500.816 1381.95,502.186 1384.77,502.186 1387.6,507.667 1390.42,503.556 1393.25,506.297 1396.07,502.186 1398.9,507.667 1401.72,499.445 \n",
       "  1404.54,496.705 1407.37,500.816 1410.19,509.037 1413.02,500.816 1415.84,500.816 1418.67,499.445 1421.49,496.705 1424.31,507.667 1427.14,493.965 1429.96,509.037 \n",
       "  1432.79,496.705 1435.61,506.297 1438.44,518.629 1441.26,498.075 1444.09,499.445 1446.91,496.705 1449.73,502.186 1452.56,502.186 1455.38,502.186 1458.21,498.075 \n",
       "  1461.03,498.075 1463.86,499.445 1466.68,495.335 1469.51,495.335 1472.33,495.335 1475.15,496.705 1477.98,493.965 1480.8,483.003 1483.63,491.224 1486.45,503.556 \n",
       "  1489.28,496.705 1492.1,488.484 1494.92,491.224 1497.75,495.335 1500.57,492.594 1503.4,492.594 1506.22,492.594 1509.05,492.594 1511.87,496.705 1514.7,492.594 \n",
       "  1517.52,488.484 1520.34,493.965 1523.17,489.854 1525.99,493.965 1528.82,493.965 1531.64,499.445 1534.47,491.224 1537.29,493.965 1540.11,493.965 1542.94,495.335 \n",
       "  1545.76,499.445 1548.59,491.224 1551.41,491.224 1554.24,488.484 1557.06,491.224 1559.89,492.594 1562.71,477.522 1565.53,489.854 1568.36,492.594 1571.18,498.075 \n",
       "  1574.01,491.224 1576.83,488.484 1579.66,481.632 1582.48,485.743 1585.31,488.484 1588.13,489.854 1590.95,491.224 1593.78,500.816 1596.6,493.965 1599.43,499.445 \n",
       "  1602.25,485.743 1605.08,496.705 1607.9,491.224 1610.72,487.113 1613.55,496.705 1616.37,485.743 1619.2,484.373 1622.02,491.224 1624.85,493.965 1627.67,495.335 \n",
       "  1630.5,487.113 1633.32,487.113 1636.14,489.854 1638.97,492.594 1641.79,491.224 1644.62,491.224 1647.44,485.743 1650.27,487.113 1653.09,484.373 1655.91,491.224 \n",
       "  1658.74,487.113 1661.56,493.965 1664.39,492.594 1667.21,481.632 1670.04,481.632 1672.86,492.594 1675.69,491.224 1678.51,488.484 1681.33,492.594 1684.16,483.003 \n",
       "  1686.98,495.335 1689.81,489.854 1692.63,484.373 1695.46,493.965 1698.28,487.113 1701.1,487.113 1703.93,487.113 1706.75,478.892 1709.58,483.003 1712.4,487.113 \n",
       "  1715.23,488.484 1718.05,474.781 1720.88,487.113 1723.7,487.113 1726.52,481.632 1729.35,483.003 1732.17,485.743 1735,487.113 1737.82,478.892 1740.65,488.484 \n",
       "  1743.47,477.522 1746.3,495.335 1749.12,478.892 1751.94,487.113 1754.77,484.373 1757.59,483.003 1760.42,481.632 1763.24,493.965 1766.07,487.113 1768.89,480.262 \n",
       "  1771.71,478.892 1774.54,484.373 1777.36,484.373 1780.19,478.892 1783.01,476.152 1785.84,473.411 1788.66,476.152 1791.49,470.671 1794.31,478.892 1797.13,481.632 \n",
       "  1799.96,483.003 1802.78,477.522 1805.61,489.854 1808.43,488.484 1811.26,478.892 1814.08,484.373 1816.9,478.892 1819.73,488.484 1822.55,480.262 1825.38,480.262 \n",
       "  1828.2,474.781 1831.03,474.781 1833.85,483.003 1836.68,480.262 1839.5,481.632 1842.32,484.373 1845.15,476.152 1847.97,481.632 1850.8,474.781 1853.62,473.411 \n",
       "  1856.45,474.781 1859.27,474.781 1862.1,480.262 1864.92,473.411 1867.74,485.743 1870.57,477.522 1873.39,476.152 1876.22,469.3 1879.04,476.152 1881.87,470.671 \n",
       "  1884.69,472.041 1887.51,481.632 1890.34,473.411 1893.16,478.892 1895.99,477.522 1898.81,474.781 1901.64,476.152 1904.46,472.041 1907.29,473.411 1910.11,476.152 \n",
       "  1912.93,476.152 1915.76,477.522 1918.58,474.781 1921.41,478.892 1924.23,477.522 1927.06,476.152 1929.88,470.671 1932.7,473.411 1935.53,474.781 1938.35,473.411 \n",
       "  1941.18,473.411 1944,469.3 1946.83,480.262 1949.65,469.3 1952.48,470.671 1955.3,474.781 1958.12,463.82 1960.95,476.152 1963.77,472.041 1966.6,476.152 \n",
       "  1969.42,463.82 1972.25,477.522 1975.07,481.632 1977.9,461.079 1980.72,476.152 1983.54,467.93 1986.37,483.003 1989.19,461.079 1992.02,461.079 1994.84,470.671 \n",
       "  1997.67,465.19 2000.49,478.892 2003.31,466.56 2006.14,463.82 2008.96,469.3 2011.79,469.3 2014.61,470.671 2017.44,470.671 2020.26,467.93 2023.09,467.93 \n",
       "  2025.91,470.671 2028.73,462.449 2031.56,462.449 2034.38,466.56 2037.21,470.671 2040.03,473.411 2042.86,462.449 2045.68,472.041 2048.5,467.93 2051.33,466.56 \n",
       "  2054.15,465.19 2056.98,470.671 2059.8,465.19 2062.63,466.56 2065.45,462.449 2068.28,476.152 2071.1,465.19 2073.92,470.671 2076.75,463.82 2079.57,465.19 \n",
       "  2082.4,469.3 2085.22,459.709 2088.05,465.19 2090.87,466.56 2093.69,469.3 2096.52,477.522 2099.34,463.82 2102.17,465.19 2104.99,466.56 2107.82,465.19 \n",
       "  2110.64,462.449 2113.47,465.19 2116.29,461.079 2119.11,462.449 2121.94,473.411 2124.76,467.93 2127.59,472.041 2130.41,470.671 2133.24,466.56 2136.06,462.449 \n",
       "  2138.89,459.709 2141.71,461.079 2144.53,467.93 2147.36,462.449 2150.18,461.079 2153.01,458.339 2155.83,465.19 2158.66,456.968 2161.48,462.449 2164.3,458.339 \n",
       "  2167.13,467.93 2169.95,462.449 2172.78,461.079 2175.6,465.19 2178.43,463.82 2181.25,458.339 2184.08,458.339 2186.9,463.82 2189.72,461.079 2192.55,461.079 \n",
       "  2195.37,459.709 2198.2,456.968 2201.02,456.968 2203.85,456.968 2206.67,459.709 2209.49,456.968 2212.32,459.709 2215.14,461.079 2217.97,456.968 2220.79,456.968 \n",
       "  2223.62,466.56 2226.44,461.079 2229.27,461.079 2232.09,458.339 2234.91,458.339 2237.74,461.079 2240.56,463.82 2243.39,459.709 2246.21,458.339 2249.04,461.079 \n",
       "  2251.86,462.449 2254.69,462.449 2257.51,469.3 2260.33,458.339 2263.16,462.449 2265.98,458.339 2268.81,455.598 2271.63,456.968 2274.46,458.339 2277.28,465.19 \n",
       "  2280.1,459.709 2282.93,458.339 2285.75,461.079 2288.58,458.339 2291.4,461.079 2294.23,456.968 2297.05,459.709 2299.88,452.858 2302.7,454.228 2305.52,450.117 \n",
       "  2308.35,459.709 2311.17,459.709 2314,458.339 2316.82,459.709 2319.65,455.598 2322.47,455.598 2325.29,454.228 2328.12,456.968 2330.94,454.228 2333.77,452.858 \n",
       "  2336.59,458.339 2339.42,452.858 2342.24,455.598 2345.07,452.858 2347.89,456.968 2350.71,447.377 2353.54,456.968 2356.36,455.598 2359.19,455.598 2362.01,451.488 \n",
       "  2364.84,455.598 2367.66,455.598 2370.49,454.228 2373.31,452.858 2376.13,454.228 2378.96,458.339 2381.78,452.858 2384.61,452.858 2387.43,452.858 2390.26,450.117 \n",
       "  2393.08,458.339 2395.9,451.488 2398.73,456.968 2401.55,455.598 2404.38,459.709 2407.2,452.858 2410.03,452.858 2412.85,448.747 2415.68,458.339 2418.5,451.488 \n",
       "  2421.32,461.079 2424.15,454.228 2426.97,450.117 2429.8,458.339 2432.62,458.339 2435.45,461.079 2438.27,452.858 2441.09,456.968 2443.92,448.747 2446.74,456.968 \n",
       "  2449.57,448.747 2452.39,446.007 2455.22,454.228 2458.04,447.377 2460.87,456.968 2463.69,452.858 2466.51,451.488 2469.34,452.858 2472.16,447.377 2474.99,447.377 \n",
       "  2477.81,454.228 2480.64,450.117 2483.46,450.117 2486.28,455.598 2489.11,451.488 2491.93,454.228 2494.76,448.747 2497.58,452.858 2500.41,444.636 2503.23,450.117 \n",
       "  2506.06,448.747 2508.88,455.598 2511.7,455.598 2514.53,459.709 2517.35,451.488 2520.18,451.488 2523,446.007 2525.83,446.007 2528.65,450.117 2531.48,448.747 \n",
       "  2534.3,446.007 2537.12,446.007 2539.95,454.228 2542.77,444.636 2545.6,448.747 2548.42,450.117 2551.25,448.747 2554.07,448.747 2556.89,441.896 2559.72,450.117 \n",
       "  2562.54,447.377 2565.37,441.896 2568.19,448.747 2571.02,446.007 2573.84,444.636 2576.67,440.526 2579.49,447.377 2582.31,447.377 2585.14,448.747 2587.96,451.488 \n",
       "  2590.79,447.377 2593.61,447.377 2596.44,446.007 2599.26,441.896 2602.08,444.636 2604.91,441.896 2607.73,451.488 2610.56,443.266 2613.38,446.007 2616.21,443.266 \n",
       "  2619.03,441.896 2621.86,443.266 2624.68,440.526 2627.5,448.747 2630.33,444.636 2633.15,446.007 2635.98,437.785 2638.8,443.266 2641.63,447.377 2644.45,439.156 \n",
       "  2647.28,439.156 2650.1,441.896 2652.92,444.636 2655.75,440.526 2658.57,440.526 2661.4,446.007 2664.22,443.266 2667.05,444.636 2669.87,440.526 2672.69,441.896 \n",
       "  2675.52,443.266 2678.34,441.896 2681.17,441.896 2683.99,440.526 2686.82,441.896 2689.64,443.266 2692.47,441.896 2695.29,451.488 2698.11,439.156 2700.94,437.785 \n",
       "  2703.76,448.747 2706.59,441.896 2709.41,437.785 2712.24,443.266 2715.06,444.636 2717.88,451.488 2720.71,441.896 2723.53,437.785 2726.36,441.896 2729.18,447.377 \n",
       "  2732.01,436.415 2734.83,439.156 2737.66,444.636 2740.48,441.896 2743.3,440.526 2746.13,441.896 2748.95,444.636 2751.78,437.785 2754.6,443.266 2757.43,443.266 \n",
       "  2760.25,440.526 2763.08,443.266 2765.9,440.526 2768.72,437.785 2771.55,444.636 2774.37,436.415 2777.2,436.415 2780.02,441.896 2782.85,437.785 2785.67,439.156 \n",
       "  2788.49,435.045 2791.32,435.045 2794.14,435.045 2796.97,440.526 2799.79,437.785 2802.62,441.896 2805.44,440.526 2808.27,437.785 2811.09,441.896 2813.91,441.896 \n",
       "  2816.74,437.785 2819.56,448.747 2822.39,433.675 2825.21,439.156 2828.04,428.194 2830.86,440.526 2833.68,437.785 2836.51,436.415 2839.33,437.785 2842.16,437.785 \n",
       "  2844.98,430.934 2847.81,439.156 2850.63,439.156 2853.46,437.785 2856.28,432.304 2859.1,436.415 2861.93,441.896 2864.75,436.415 2867.58,432.304 2870.4,437.785 \n",
       "  2873.23,435.045 2876.05,437.785 2878.87,435.045 2881.7,437.785 2884.52,439.156 2887.35,441.896 2890.17,435.045 2893,441.896 2895.82,435.045 2898.65,433.675 \n",
       "  2901.47,432.304 2904.29,435.045 2907.12,432.304 2909.94,436.415 2912.77,436.415 2915.59,441.896 2918.42,432.304 2921.24,435.045 2924.07,437.785 2926.89,435.045 \n",
       "  2929.71,439.156 2932.54,433.675 2935.36,440.526 2938.19,437.785 2941.01,433.675 2943.84,430.934 2946.66,441.896 2949.48,433.675 2952.31,436.415 2955.13,435.045 \n",
       "  2957.96,435.045 2960.78,439.156 2963.61,433.675 2966.43,440.526 2969.26,450.117 2972.08,436.415 2974.9,428.194 2977.73,433.675 2980.55,437.785 2983.38,439.156 \n",
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       "  3042.69,433.675 3045.51,436.415 3048.34,435.045 3051.16,430.934 3053.99,435.045 3056.81,428.194 3059.64,435.045 3062.46,430.934 3065.28,432.304 3068.11,435.045 \n",
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       "  274.789,2102.61 277.613,2084.79 280.438,2121.79 283.262,2083.42 286.086,2091.65 288.911,2098.5 291.735,2061.5 294.56,2056.02 297.384,2032.73 300.208,2013.54 \n",
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       "  387.764,1827.19 390.589,1765.53 393.413,1792.94 396.237,1787.46 399.062,1772.38 401.886,1761.42 404.711,1749.09 407.535,1754.57 410.359,1739.5 413.184,1739.5 \n",
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       "  754.935,1348.98 757.759,1348.98 760.584,1343.5 763.408,1342.13 766.232,1343.5 769.057,1346.24 771.881,1350.35 774.706,1354.47 777.53,1324.32 780.354,1343.5 \n",
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       "  924.398,1301.03 927.223,1318.84 930.047,1294.18 932.871,1309.25 935.696,1276.36 938.52,1303.77 941.344,1283.21 944.169,1302.4 946.993,1309.25 949.818,1302.4 \n",
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       "  980.886,1309.25 983.71,1268.14 986.535,1290.06 989.359,1284.58 992.183,1296.92 995.008,1296.92 997.832,1285.95 1000.66,1279.1 1003.48,1301.03 1006.31,1287.32 \n",
       "  1009.13,1291.43 1011.95,1283.21 1014.78,1292.81 1017.6,1296.92 1020.43,1296.92 1023.25,1288.69 1026.08,1284.58 1028.9,1287.32 1031.72,1279.1 1034.55,1281.84 \n",
       "  1037.37,1277.73 1040.2,1266.77 1043.02,1262.66 1045.85,1272.25 1048.67,1290.06 1051.5,1283.21 1054.32,1281.84 1057.14,1270.88 1059.97,1283.21 1062.79,1272.25 \n",
       "  1065.62,1279.1 1068.44,1272.25 1071.27,1295.55 1074.09,1298.29 1076.92,1274.99 1079.74,1265.4 1082.56,1283.21 1085.39,1281.84 1088.21,1272.25 1091.04,1284.58 \n",
       "  1093.86,1269.51 1096.69,1270.88 1099.51,1283.21 1102.33,1274.99 1105.16,1261.29 1107.98,1274.99 1110.81,1274.99 1113.63,1265.4 1116.46,1259.92 1119.28,1274.99 \n",
       "  1122.11,1259.92 1124.93,1270.88 1127.75,1269.51 1130.58,1253.07 1133.4,1253.07 1136.23,1251.7 1139.05,1240.74 1141.88,1272.25 1144.7,1255.81 1147.52,1257.18 \n",
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       "  1178.59,1240.74 1181.42,1257.18 1184.24,1276.36 1187.07,1251.7 1189.89,1240.74 1192.72,1266.77 1195.54,1261.29 1198.36,1248.96 1201.19,1251.7 1204.01,1253.07 \n",
       "  1206.84,1243.48 1209.66,1253.07 1212.49,1242.11 1215.31,1250.33 1218.13,1238 1220.96,1253.07 1223.78,1239.37 1226.61,1261.29 1229.43,1243.48 1232.26,1248.96 \n",
       "  1235.08,1250.33 1237.91,1250.33 1240.73,1228.4 1243.55,1232.52 1246.38,1248.96 1249.2,1232.52 1252.03,1228.4 1254.85,1239.37 1257.68,1238 1260.5,1239.37 \n",
       "  1263.32,1238 1266.15,1247.59 1268.97,1239.37 1271.8,1216.07 1274.62,1232.52 1277.45,1221.55 1280.27,1227.03 1283.1,1224.29 1285.92,1231.15 1288.74,1229.77 \n",
       "  1291.57,1238 1294.39,1239.37 1297.22,1222.92 1300.04,1233.89 1302.87,1218.81 1305.69,1229.77 1308.51,1221.55 1311.34,1218.81 1314.16,1222.92 1316.99,1225.66 \n",
       "  1319.81,1233.89 1322.64,1231.15 1325.46,1213.33 1328.29,1218.81 1331.11,1207.85 1333.93,1213.33 1336.76,1220.18 1339.58,1209.22 1342.41,1210.59 1345.23,1216.07 \n",
       "  1348.06,1225.66 1350.88,1217.44 1353.71,1217.44 1356.53,1218.81 1359.35,1218.81 1362.18,1211.96 1365,1209.22 1367.83,1203.74 1370.65,1218.81 1373.48,1222.92 \n",
       "  1376.3,1220.18 1379.12,1220.18 1381.95,1202.37 1384.77,1195.52 1387.6,1199.63 1390.42,1201 1393.25,1213.33 1396.07,1202.37 1398.9,1207.85 1401.72,1216.07 \n",
       "  1404.54,1214.7 1407.37,1224.29 1410.19,1209.22 1413.02,1209.22 1415.84,1209.22 1418.67,1220.18 1421.49,1210.59 1424.31,1216.07 1427.14,1203.74 1429.96,1207.85 \n",
       "  1432.79,1213.33 1435.61,1218.81 1438.44,1217.44 1441.26,1213.33 1444.09,1218.81 1446.91,1199.63 1449.73,1201 1452.56,1211.96 1455.38,1209.22 1458.21,1196.89 \n",
       "  1461.03,1211.96 1463.86,1217.44 1466.68,1210.59 1469.51,1199.63 1472.33,1203.74 1475.15,1201 1477.98,1214.7 1480.8,1213.33 1483.63,1206.48 1486.45,1210.59 \n",
       "  1489.28,1211.96 1492.1,1203.74 1494.92,1185.93 1497.75,1196.89 1500.57,1211.96 1503.4,1201 1506.22,1207.85 1509.05,1210.59 1511.87,1202.37 1514.7,1209.22 \n",
       "  1517.52,1198.26 1520.34,1201 1523.17,1205.11 1525.99,1195.52 1528.82,1191.41 1531.64,1199.63 1534.47,1190.04 1537.29,1196.89 1540.11,1188.67 1542.94,1201 \n",
       "  1545.76,1196.89 1548.59,1192.78 1551.41,1202.37 1554.24,1185.93 1557.06,1213.33 1559.89,1179.08 1562.71,1188.67 1565.53,1185.93 1568.36,1194.15 1571.18,1183.19 \n",
       "  1574.01,1199.63 1576.83,1195.52 1579.66,1184.56 1582.48,1177.71 1585.31,1179.08 1588.13,1187.3 1590.95,1188.67 1593.78,1198.26 1596.6,1187.3 1599.43,1187.3 \n",
       "  1602.25,1183.19 1605.08,1184.56 1607.9,1180.45 1610.72,1196.89 1613.55,1184.56 1616.37,1184.56 1619.2,1181.82 1622.02,1181.82 1624.85,1177.71 1627.67,1188.67 \n",
       "  1630.5,1185.93 1633.32,1185.93 1636.14,1198.26 1638.97,1180.45 1641.79,1188.67 1644.62,1194.15 1647.44,1185.93 1650.27,1180.45 1653.09,1181.82 1655.91,1184.56 \n",
       "  1658.74,1179.08 1661.56,1183.19 1664.39,1188.67 1667.21,1198.26 1670.04,1201 1672.86,1180.45 1675.69,1183.19 1678.51,1194.15 1681.33,1180.45 1684.16,1180.45 \n",
       "  1686.98,1176.34 1689.81,1185.93 1692.63,1191.41 1695.46,1179.08 1698.28,1191.41 1701.1,1181.82 1703.93,1180.45 1706.75,1177.71 1709.58,1173.6 1712.4,1183.19 \n",
       "  1715.23,1192.78 1718.05,1179.08 1720.88,1185.93 1723.7,1179.08 1726.52,1183.19 1729.35,1176.34 1732.17,1179.08 1735,1184.56 1737.82,1172.23 1740.65,1166.74 \n",
       "  1743.47,1179.08 1746.3,1169.48 1749.12,1194.15 1751.94,1191.41 1754.77,1179.08 1757.59,1174.97 1760.42,1173.6 1763.24,1173.6 1766.07,1183.19 1768.89,1181.82 \n",
       "  1771.71,1177.71 1774.54,1179.08 1777.36,1168.11 1780.19,1195.52 1783.01,1180.45 1785.84,1177.71 1788.66,1172.23 1791.49,1168.11 1794.31,1174.97 1797.13,1164 \n",
       "  1799.96,1174.97 1802.78,1169.48 1805.61,1168.11 1808.43,1168.11 1811.26,1165.37 1814.08,1179.08 1816.9,1172.23 1819.73,1161.26 1822.55,1165.37 1825.38,1158.52 \n",
       "  1828.2,1161.26 1831.03,1177.71 1833.85,1181.82 1836.68,1172.23 1839.5,1169.48 1842.32,1161.26 1845.15,1159.89 1847.97,1161.26 1850.8,1162.63 1853.62,1173.6 \n",
       "  1856.45,1158.52 1859.27,1164 1862.1,1164 1864.92,1165.37 1867.74,1162.63 1870.57,1158.52 1873.39,1161.26 1876.22,1164 1879.04,1183.19 1881.87,1170.86 \n",
       "  1884.69,1162.63 1887.51,1161.26 1890.34,1173.6 1893.16,1155.78 1895.99,1162.63 1898.81,1168.11 1901.64,1165.37 1904.46,1165.37 1907.29,1157.15 1910.11,1155.78 \n",
       "  1912.93,1155.78 1915.76,1170.86 1918.58,1162.63 1921.41,1179.08 1924.23,1151.67 1927.06,1169.48 1929.88,1158.52 1932.7,1161.26 1935.53,1157.15 1938.35,1157.15 \n",
       "  1941.18,1166.74 1944,1161.26 1946.83,1155.78 1949.65,1153.04 1952.48,1174.97 1955.3,1150.3 1958.12,1158.52 1960.95,1158.52 1963.77,1147.56 1966.6,1153.04 \n",
       "  1969.42,1154.41 1972.25,1159.89 1975.07,1158.52 1977.9,1154.41 1980.72,1155.78 1983.54,1165.37 1986.37,1157.15 1989.19,1151.67 1992.02,1162.63 1994.84,1147.56 \n",
       "  1997.67,1158.52 2000.49,1154.41 2003.31,1153.04 2006.14,1147.56 2008.96,1165.37 2011.79,1161.26 2014.61,1153.04 2017.44,1153.04 2020.26,1155.78 2023.09,1150.3 \n",
       "  2025.91,1143.45 2028.73,1150.3 2031.56,1159.89 2034.38,1142.08 2037.21,1153.04 2040.03,1153.04 2042.86,1146.19 2045.68,1146.19 2048.5,1162.63 2051.33,1148.93 \n",
       "  2054.15,1146.19 2056.98,1155.78 2059.8,1143.45 2062.63,1158.52 2065.45,1159.89 2068.28,1155.78 2071.1,1147.56 2073.92,1157.15 2076.75,1146.19 2079.57,1142.08 \n",
       "  2082.4,1153.04 2085.22,1147.56 2088.05,1150.3 2090.87,1154.41 2093.69,1140.71 2096.52,1142.08 2099.34,1150.3 2102.17,1153.04 2104.99,1142.08 2107.82,1148.93 \n",
       "  2110.64,1153.04 2113.47,1155.78 2116.29,1148.93 2119.11,1154.41 2121.94,1153.04 2124.76,1140.71 2127.59,1143.45 2130.41,1136.6 2133.24,1146.19 2136.06,1147.56 \n",
       "  2138.89,1144.82 2141.71,1147.56 2144.53,1146.19 2147.36,1153.04 2150.18,1136.6 2153.01,1139.34 2155.83,1142.08 2158.66,1143.45 2161.48,1162.63 2164.3,1159.89 \n",
       "  2167.13,1143.45 2169.95,1144.82 2172.78,1147.56 2175.6,1146.19 2178.43,1146.19 2181.25,1147.56 2184.08,1142.08 2186.9,1146.19 2189.72,1140.71 2192.55,1133.86 \n",
       "  2195.37,1131.12 2198.2,1136.6 2201.02,1144.82 2203.85,1147.56 2206.67,1148.93 2209.49,1140.71 2212.32,1155.78 2215.14,1140.71 2217.97,1143.45 2220.79,1146.19 \n",
       "  2223.62,1144.82 2226.44,1142.08 2229.27,1144.82 2232.09,1146.19 2234.91,1147.56 2237.74,1146.19 2240.56,1148.93 2243.39,1137.97 2246.21,1143.45 2249.04,1135.23 \n",
       "  2251.86,1151.67 2254.69,1147.56 2257.51,1135.23 2260.33,1137.97 2263.16,1140.71 2265.98,1142.08 2268.81,1135.23 2271.63,1135.23 2274.46,1146.19 2277.28,1137.97 \n",
       "  2280.1,1135.23 2282.93,1132.49 2285.75,1136.6 2288.58,1136.6 2291.4,1137.97 2294.23,1137.97 2297.05,1144.82 2299.88,1143.45 2302.7,1139.34 2305.52,1129.75 \n",
       "  2308.35,1139.34 2311.17,1131.12 2314,1136.6 2316.82,1133.86 2319.65,1136.6 2322.47,1131.12 2325.29,1132.49 2328.12,1136.6 2330.94,1143.45 2333.77,1144.82 \n",
       "  2336.59,1133.86 2339.42,1132.49 2342.24,1147.56 2345.07,1127.01 2347.89,1136.6 2350.71,1131.12 2353.54,1140.71 2356.36,1135.23 2359.19,1133.86 2362.01,1124.27 \n",
       "  2364.84,1131.12 2367.66,1140.71 2370.49,1135.23 2373.31,1127.01 2376.13,1136.6 2378.96,1121.53 2381.78,1136.6 2384.61,1128.38 2387.43,1125.64 2390.26,1122.9 \n",
       "  2393.08,1121.53 2395.9,1129.75 2398.73,1132.49 2401.55,1128.38 2404.38,1120.16 2407.2,1125.64 2410.03,1125.64 2412.85,1122.9 2415.68,1118.79 2418.5,1121.53 \n",
       "  2421.32,1122.9 2424.15,1129.75 2426.97,1127.01 2429.8,1129.75 2432.62,1129.75 2435.45,1129.75 2438.27,1127.01 2441.09,1133.86 2443.92,1133.86 2446.74,1135.23 \n",
       "  2449.57,1129.75 2452.39,1127.01 2455.22,1117.42 2458.04,1124.27 2460.87,1129.75 2463.69,1139.34 2466.51,1135.23 2469.34,1128.38 2472.16,1122.9 2474.99,1143.45 \n",
       "  2477.81,1136.6 2480.64,1111.94 2483.46,1132.49 2486.28,1127.01 2489.11,1128.38 2491.93,1122.9 2494.76,1127.01 2497.58,1121.53 2500.41,1136.6 2503.23,1122.9 \n",
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       "  3014.45,1110.57 3017.27,1110.57 3020.09,1105.08 3022.92,1107.82 3025.74,1111.94 3028.57,1113.31 3031.39,1109.2 3034.22,1107.82 3037.04,1110.57 3039.87,1106.45 \n",
       "  3042.69,1111.94 3045.51,1105.08 3048.34,1100.97 3051.16,1096.86 3053.99,1110.57 3056.81,1102.34 3059.64,1105.08 3062.46,1103.71 3065.28,1113.31 3068.11,1105.08 \n",
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       "  274.789,1969.7 277.613,1980.66 280.438,1962.84 283.262,1943.66 286.086,1962.84 288.911,1943.66 291.735,1950.51 294.56,1946.4 297.384,1939.55 300.208,1924.48 \n",
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       "  1517.52,1758.68 1520.34,1761.42 1523.17,1761.42 1525.99,1761.42 1528.82,1760.05 1531.64,1764.16 1534.47,1762.79 1537.29,1761.42 1540.11,1761.42 1542.94,1758.68 \n",
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       "  1602.25,1755.94 1605.08,1753.2 1607.9,1754.57 1610.72,1755.94 1613.55,1755.94 1616.37,1758.68 1619.2,1758.68 1622.02,1757.31 1624.85,1758.68 1627.67,1754.57 \n",
       "  1630.5,1757.31 1633.32,1755.94 1636.14,1754.57 1638.97,1755.94 1641.79,1754.57 1644.62,1755.94 1647.44,1757.31 1650.27,1757.31 1653.09,1754.57 1655.91,1755.94 \n",
       "  1658.74,1755.94 1661.56,1754.57 1664.39,1757.31 1667.21,1760.05 1670.04,1755.94 1672.86,1758.68 1675.69,1754.57 1678.51,1758.68 1681.33,1755.94 1684.16,1757.31 \n",
       "  1686.98,1755.94 1689.81,1761.42 1692.63,1755.94 1695.46,1755.94 1698.28,1754.57 1701.1,1757.31 1703.93,1757.31 1706.75,1755.94 1709.58,1753.2 1712.4,1754.57 \n",
       "  1715.23,1754.57 1718.05,1758.68 1720.88,1757.31 1723.7,1757.31 1726.52,1754.57 1729.35,1755.94 1732.17,1754.57 1735,1755.94 1737.82,1757.31 1740.65,1757.31 \n",
       "  1743.47,1754.57 1746.3,1751.83 1749.12,1755.94 1751.94,1751.83 1754.77,1750.46 1757.59,1753.2 1760.42,1753.2 1763.24,1751.83 1766.07,1749.09 1768.89,1751.83 \n",
       "  1771.71,1749.09 1774.54,1749.09 1777.36,1751.83 1780.19,1751.83 1783.01,1753.2 1785.84,1749.09 1788.66,1753.2 1791.49,1751.83 1794.31,1750.46 1797.13,1754.57 \n",
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       "  1828.2,1750.46 1831.03,1751.83 1833.85,1750.46 1836.68,1750.46 1839.5,1747.72 1842.32,1747.72 1845.15,1746.35 1847.97,1749.09 1850.8,1753.2 1853.62,1749.09 \n",
       "  1856.45,1749.09 1859.27,1749.09 1862.1,1749.09 1864.92,1750.46 1867.74,1749.09 1870.57,1749.09 1873.39,1749.09 1876.22,1749.09 1879.04,1747.72 1881.87,1750.46 \n",
       "  1884.69,1749.09 1887.51,1749.09 1890.34,1751.83 1893.16,1749.09 1895.99,1749.09 1898.81,1750.46 1901.64,1749.09 1904.46,1750.46 1907.29,1751.83 1910.11,1747.72 \n",
       "  1912.93,1749.09 1915.76,1746.35 1918.58,1749.09 1921.41,1750.46 1924.23,1746.35 1927.06,1750.46 1929.88,1747.72 1932.7,1747.72 1935.53,1749.09 1938.35,1746.35 \n",
       "  1941.18,1747.72 1944,1747.72 1946.83,1746.35 1949.65,1749.09 1952.48,1746.35 1955.3,1747.72 1958.12,1750.46 1960.95,1747.72 1963.77,1749.09 1966.6,1749.09 \n",
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     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "truereward = 4.0\n",
    "\n",
    "p = plot(legend=:bottomright)\n",
    "\n",
    "plot!(p, mean(gb_bandit_testbed(;opt=Descent(0.1), baseline=SampleAvg(), truereward=truereward)[2] for _ in 1:2000), label=\"alpha = 0.1, with baseline\")\n",
    "plot!(p, mean(gb_bandit_testbed(;opt=Descent(0.4), baseline=SampleAvg(), truereward=truereward)[2] for _ in 1:2000), label=\"alpha = 0.4, with baseline\")\n",
    "plot!(p, mean(gb_bandit_testbed(;opt=Descent(0.1), truereward=truereward)[2] for _ in 1:2000), label=\"alpha = 0.1, without baseline\")\n",
    "plot!(p, mean(gb_bandit_testbed(;opt=Descent(0.4), truereward=truereward)[2] for _ in 1:2000), label=\"alpha = 0.4, without baseline\")\n",
    "\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:00\u001b[39m\n"
     ]
    },
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     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(legend=:topleft)\n",
    "\n",
    "plot!(p, -7:-2, [mean(mean(bandit_testbed(;explorer=EpsilonGreedyExplorer(2.0^i))[1] for _ in 1:2000)) for i in -7:-2], label=\"epsilon greedy\")\n",
    "plot!(p, -5:1, [mean(mean(gb_bandit_testbed(;explorer=WeightedExplorer(is_normalized=true), opt=Descent(2.0^i))[1] for _ in 1:2000)) for i in -5:1], label=\"gradient\")\n",
    "plot!(p, -4:2, [mean(mean(bandit_testbed(;explorer=UCBExplorer(10; c=2.0^i))[1] for _ in 1:2000)) for i in -4:2], label=\"UCB\")\n",
    "plot!(p, -2:2, [mean(mean(bandit_testbed(;explorer=EpsilonGreedyExplorer(0.), init=(2.0^i))[1] for _ in 1:2000)) for i in -2:2], label=\"greedy with initialization\")\n",
    "\n",
    "p"
   ]
  }
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